When two straight lines cross, what is true of the angles opposite each other?

They are equal , and are called vertically opposite angles. Two crossing lines produce two such pairs, one pair on each side of the crossing point.

Why are vertically opposite angles equal?

Each of the two makes a straight line with the same neighbouring angle, so each of them is 180° minus that neighbour. Two quantities equal to the same thing have to be equal to each other.

True or False? Angles around a point always add up to 360°, however many of them there are.

True. The angles fill one complete turn about the point, and a complete turn is 360° whatever number of angles it has been divided into. So three angles about a point add to 360°, and so do seven.

Which two angles of an isosceles triangle are equal?

The equal angles are the two opposite the two sides of equal length . Working out which pair they are is most of the task, since the remaining angle is the odd one out.

True or False? A triangle can have two right angles.

False. Two right angles already account for 180°, which is the whole of the angle sum, leaving nothing at all for the third angle. A triangle can have at most one right angle.

What are the four interior angles of a square or a rectangle?

All four of them are right angles of 90° each. Four lots of 90° come to 360°, which is exactly the total the four angles of any quadrilateral have to reach.

What is true of the angles of a parallelogram or a rhombus?

Opposite angles are equal, so the four angles form two matching pairs. Each pair of adjacent angles adds up to 180°, which follows from the two matching pairs together making 360°.

How many pairs of equal angles does a kite have?

Just one pair, and they are the two opposite angles that each sit between a long side and a short side. The other two angles are generally different from each other and from that pair.

True or False? The four angles of a quadrilateral add up to 360° only if the quadrilateral is a regular one.

False. The four interior angles add up to 360° in every quadrilateral, regular or not. An irregular quadrilateral with angles of 97°, 115° and 85° must therefore have a fourth angle of 63°.

True or False? The sum of the exterior angles in any polygon always adds up to 360° .

True. The sum of the exterior angles in any polygon always adds up to 360° .

True or False? The sum of an interior angle and an exterior angle at the same vertex on a polygon is equal to 180° .

True. The sum of an interior angle and an exterior angle at the same vertex on a polygon is equal to 180° .

What is a regular polygon ?

A regular polygon is a polygon where all sides are equal and all angles are equal .

True or False? An irregular polygon can have more than one side of the same length .

True. An irregular polygon can have more than one side of the same length . It is an irregular polygon unless all sides are the same length and all angles are the same size, in which case it would be a regular polygon.

True or False? The sum of interior angles in a regular polygon is different to the sum of interior angles in an irregular polygon with the same number of sides.

False. The sum of interior angles in a regular polygon is the same as the sum of interior angles in an irregular polygon with the same number of sides. The sum of interior angles is dependent on the number of sides . It is not dependent on whether the polygon is regular or irregular.

What are parallel lines ?

Parallel lines are lines that are always equidistant (i.e. the same distance apart) and never meet .

What is a transverse line ?

A transverse line is a straight line that extends across two parallel lines .

True or False? In an exam question involving the use of angle facts, you should state the appropriate angle fact as well as the size of the relevant angle .

True. To get full marks in an exam you will need to write down the size of any angles that you have found but you will also need to give reasons . Make sure that you use the correct terminology for the different angle facts.

O LevelMathsCambridge (CIE)FlashcardsGeometryAngles in Polygons & Parallel Lines

Angles in Polygons & Parallel Lines (Cambridge (CIE) O Level Maths): Flashcards

Exam code: 4024

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FrontAngles around Points & Lines
Complete the two basic angle facts:
Angles that meet around a point add up to one complete $______$ of 360 degrees, while angles that meet on a straight line add up to $______$ degrees instead.

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Cards in this collection (29)

Complete the two basic angle facts:
Angles that meet around a point add up to one complete $______$ of 360 degrees, while angles that meet on a straight line add up to $______$ degrees instead.
The completed facts are:
Angles that meet around a point add up to one complete turn of 360 degrees, while angles that meet on a straight line add up to 180 degrees instead.
When two straight lines cross, what is true of the angles opposite each other?
They are equal, and are called vertically opposite angles.
Two crossing lines produce two such pairs, one pair on each side of the crossing point.
Why are vertically opposite angles equal?
Each of the two makes a straight line with the same neighbouring angle, so each of them is 180° minus that neighbour.
Two quantities equal to the same thing have to be equal to each other.
Angles of 25°, 98° and $y$ lie side by side on one side of a straight line. What is $y$ ?
The three angles together make up the straight line, so $25 + 98 + y = 180$ and therefore $y = 57$ .
The angle is $57 °$ in total.
True or False?
Angles around a point always add up to 360°, however many of them there are.
True.
The angles fill one complete turn about the point, and a complete turn is 360° whatever number of angles it has been divided into.
So three angles about a point add to 360°, and so do seven.
Complete the angle fact for a triangle:
The three $______$ angles inside any triangle add up to $______$ degrees, whatever the shape of the triangle happens to be.
The completed fact is:
The three interior angles inside any triangle add up to 180 degrees, whatever the shape of the triangle happens to be.
Which two angles of an isosceles triangle are equal?
The equal angles are the two opposite the two sides of equal length.
Working out which pair they are is most of the task, since the remaining angle is the odd one out.
Why is every angle of an equilateral triangle 60°?
All three sides are equal, so all three angles are equal as well.
Three equal angles sharing a total of 180° must each be $180 \div 3 = 60$ degrees.
A triangle has angles of 60° and 50°. What is the third angle?
The three interior angles add up to 180°, so the third angle is $180 - 60 - 50 = 70$ degrees.
Once two angles are known the third never needs anything more than a subtraction.
True or False?
A triangle can have two right angles.
False.
Two right angles already account for 180°, which is the whole of the angle sum, leaving nothing at all for the third angle.
A triangle can have at most one right angle.
Complete the angle fact for a quadrilateral:
The four interior angles inside any quadrilateral add up to $______$ degrees, which is twice the total for a $______$ instead.
The completed fact is:
The four interior angles inside any quadrilateral add up to 360 degrees, which is twice the total for a triangle instead.
The two totals are related because a single diagonal splits any quadrilateral into two triangles.
What are the four interior angles of a square or a rectangle?
All four of them are right angles of 90° each.
Four lots of 90° come to 360°, which is exactly the total the four angles of any quadrilateral have to reach.
What is true of the angles of a parallelogram or a rhombus?
Opposite angles are equal, so the four angles form two matching pairs.
Each pair of adjacent angles adds up to 180°, which follows from the two matching pairs together making 360°.
How many pairs of equal angles does a kite have?
Just one pair, and they are the two opposite angles that each sit between a long side and a short side.
The other two angles are generally different from each other and from that pair.
True or False?
The four angles of a quadrilateral add up to 360° only if the quadrilateral is a regular one.
False.
The four interior angles add up to 360° in every quadrilateral, regular or not.
An irregular quadrilateral with angles of 97°, 115° and 85° must therefore have a fourth angle of 63°.
An interior angle of a quadrilateral is 63°, and the angle $y$ beside it lies on the same straight line. What is $y$ ?
Angles on a straight line add up to 180°, so $y = 180 - 63 = 117$ degrees.
The angle outside the quadrilateral is not one of the four interior angles, so the 360° total does not apply to it.
What is a polygon?
A polygon is a flat (plane) shape with $n$ straight sides.
E.g. a quadrilateral is a 4-sided polygon.
True or False?
The sum of the exterior angles in any polygon always adds up to 360°.
True.
The sum of the exterior angles in any polygon always adds up to 360°.
True or False?
The sum of an interior angle and an exterior angle at the same vertex on a polygon is equal to 180°.
True.
The sum of an interior angle and an exterior angle at the same vertex on a polygon is equal to 180°.
State the equation in terms of the number of sides of a polygon, $n$ , for the sum of interior angles in a polygon.
The equation in terms of the number of sides of a polygon, $n$ , for the sum of interior angles in a polygon is:
Sum of interior angles = $180 \times (n - 2)$ .
What is a regular polygon?
A regular polygon is a polygon where all sides are equal and all angles are equal.
True or False?
An irregular polygon can have more than one side of the same length.
True.
An irregular polygon can have more than one side of the same length.
It is an irregular polygon unless all sides are the same length and all angles are the same size, in which case it would be a regular polygon.
True or False?
The sum of interior angles in a regular polygon is different to the sum of interior angles in an irregular polygon with the same number of sides.
False.
The sum of interior angles in a regular polygon is the same as the sum of interior angles in an irregular polygon with the same number of sides.
The sum of interior angles is dependent on the number of sides.
It is not dependent on whether the polygon is regular or irregular.
What are parallel lines?
Parallel lines are lines that are always equidistant (i.e. the same distance apart) and never meet.
What is a transverse line?
A transverse line is a straight line that extends across two parallel lines.
What are corresponding angles?
Corresponding angles are equal angles in corresponding positions.
What are co-interior (supplementary) angles?
Co-interior (supplementary) angles are a pair of angles that are formed between a pair of parallel lines and a transverse line. Co-interior angles sum to 180^o.
What angle fact is represented by the diagram below?
Alternate angles are equal angles.
True or False?
In an exam question involving the use of angle facts, you should state the appropriate angle fact as well as the size of the relevant angle.
True.
To get full marks in an exam you will need to write down the size of any angles that you have found but you will also need to give reasons.
Make sure that you use the correct terminology for the different angle facts.

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