What are vertically opposite angles, and what is true of them?

They are the pairs of angles facing each other where two straight lines cross. Vertically opposite angles are always equal .

True or False? When two straight lines cross, all four of the angles formed are equal.

False. Only the pairs facing each other are equal. Angles that sit next to each other are on a straight line, so they add to 180° instead, and they are equal only in the special case where every angle is 90°.

What do the three interior angles of any triangle add up to?

They always add up to 180°. This holds for every triangle, whatever its shape or size.

In an isosceles triangle, which two angles are the equal ones?

The two angles opposite the two sides of equal length . It is the position relative to the equal sides that decides it, not where the triangle happens to be drawn on the page.

True or False? A right-angled triangle can also be isosceles.

True. A triangle with angles of 90°, 45° and 45° is both. The names describe different things, one the presence of a right angle and the other a pair of equal sides, so a triangle can satisfy both at once.

What do the four interior angles of any quadrilateral add up to?

They always add up to 360° . This holds for every quadrilateral, however irregular its shape.

What is true of every angle in a square or a rectangle ?

Every one of the four angles is a right angle, 90° . Four lots of 90° make the 360° that any quadrilateral must total.

In a parallelogram or a rhombus , which angles are equal?

The opposite angles are equal, giving two pairs of equal angles. The angles next to each other are not equal unless the shape happens to be a rectangle or a square.

How many pairs of equal opposite angles does a kite have?

Just one pair. The two angles between the pairs of equal sides are the equal ones, and the other two angles are generally different from each other.

True or False? Every quadrilateral has at least one pair of equal angles.

False. An irregular quadrilateral can have four angles that are all different from one another. Equal angles come from a shape's symmetry, and an irregular quadrilateral has none.

IGCSEMathsCambridge (CIE)CoreFlashcardsGeometryBasic Angle Properties

Basic Angle Properties (Cambridge (CIE) IGCSE Maths: Core): Flashcards

Exam code: 0580 & 0980

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FrontAngles around Points & Lines
Complete the two basic angle facts by filling in the missing numbers:
Angles around a point add up to $______$ °.
Angles on a straight line add up to $______$ °.

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Cards in this collection (16)

Complete the two basic angle facts by filling in the missing numbers:
Angles around a point add up to $______$ °.
Angles on a straight line add up to $______$ °.
The completed facts are:
Angles around a point add up to 360°.
Angles on a straight line add up to 180°.
What are vertically opposite angles, and what is true of them?
They are the pairs of angles facing each other where two straight lines cross.
Vertically opposite angles are always equal.
Two of the angles on a straight line are 25° and 98°. What is the third angle on that line?
The third angle is 57°.
The three angles must total 180°, and $180 - 25 - 98 = 57$ .
Three angles meet around a point. Two of them are 120° and 95°. What is the third?
The third angle is 145°.
Angles around a point total 360°, and $360 - 120 - 95 = 145$ .
True or False?
When two straight lines cross, all four of the angles formed are equal.
False.
Only the pairs facing each other are equal.
Angles that sit next to each other are on a straight line, so they add to 180° instead, and they are equal only in the special case where every angle is 90°.
What do the three interior angles of any triangle add up to?
They always add up to 180°.
This holds for every triangle, whatever its shape or size.
In an isosceles triangle, which two angles are the equal ones?
The two angles opposite the two sides of equal length.
It is the position relative to the equal sides that decides it, not where the triangle happens to be drawn on the page.
Complete the two angle facts by filling in the missing numbers:
Every angle in an equilateral triangle is $______$ °.
A right-angled triangle has one angle of $______$ °.
The completed facts are:
Every angle in an equilateral triangle is 60°.
A right-angled triangle has one angle of 90°.
In an equilateral triangle all three angles are equal, so each one is $180 \div 3$ .
True or False?
A right-angled triangle can also be isosceles.
True.
A triangle with angles of 90°, 45° and 45° is both.
The names describe different things, one the presence of a right angle and the other a pair of equal sides, so a triangle can satisfy both at once.
An isosceles triangle has two angles of 70°. What is its third angle?
The third angle is 40°.
The three angles total 180°, so the remaining angle is $180 - 70 - 70 = 40$ .
What do the four interior angles of any quadrilateral add up to?
They always add up to 360°.
This holds for every quadrilateral, however irregular its shape.
What is true of every angle in a square or a rectangle?
Every one of the four angles is a right angle, 90°.
Four lots of 90° make the 360° that any quadrilateral must total.
In a parallelogram or a rhombus, which angles are equal?
The opposite angles are equal, giving two pairs of equal angles.
The angles next to each other are not equal unless the shape happens to be a rectangle or a square.
How many pairs of equal opposite angles does a kite have?
Just one pair.
The two angles between the pairs of equal sides are the equal ones, and the other two angles are generally different from each other.
Three angles of a quadrilateral are 97°, 115° and 85°. Complete the working for the fourth:
$360 -______=______$ °
The completed working is:
$360 - 297 = 63$ °
The three given angles total $97 + 115 + 85 = 297$ .
True or False?
Every quadrilateral has at least one pair of equal angles.
False.
An irregular quadrilateral can have four angles that are all different from one another.
Equal angles come from a shape's symmetry, and an irregular quadrilateral has none.

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