Angles in Polygons & Parallel Lines (OCR GCSE Maths: Foundation): Exam Questions

The diagram shows an isosceles triangle and a straight line.
Work out the value of $w$.

$w=$...............................[2]

The diagram shows triangle $PQR$.

The side $QR$ is extended to point $S$.

Angle $QPR=65°$ and angle $PQR=80°$.

Find the size of angle $PRQ$.

Find the size of angle $PRS$.

Work out the value of $w.$
Give reasons for your answer.

$w=$ ............................ because ....................................................................................................

$QRS$is an isosceles triangle and $PQR$ is a straight line.

Find the value of $z$.

$z$ = ................................................... 

$ABC$ is an isosceles triangle.
$BCD$ is a straight line.

Find the value of $a$.

$a$ = .............................................. 

$ABC$is a straight line and $BCD$ is an isosceles triangle.
Find the value of$x$.

$x$= ................................................. 

In the triangle $ABC,AB=AC$ and angle $BAC=38°$.

$BCD$is a straight line.

Work out angle $ACD$.

Angle $ACD$ = .................................................. 

A triangle is isosceles.
One of its angles is 96°.

Find the other two angles.

........................ and ........................ 

Find the value of $x$.

$x$ = ................................................... 

The diagram shows a triangle drawn between a pair of parallel lines.

Find the value of $x$ and the value of $y$.

$$\begin{gathered} x=.............................. \\ y=.............................. \end{gathered}$$

A regular polygon has an exterior angle of 20°.

Work out the number of sides of this polygon.

The diagram shows two parallel lines and two straight lines.

i) Find the value of $a$.

Give a reason for your answer.

a = ................ because ..................................................................................................... [2]

ii) Find the value of $b$.
Give a reason for your answer.

b = ................ because ......................................................................................................[2]

iii) Find the value of $c$.

$c$ = ................................................. [2]

In the diagram, $AB$ is parallel to $CD$.

Find the value of$x$.
Give a geometrical reason for your answer.

$x$= ......................... because ....................................

Work out the value of $y$.
Give a geometrical reason for your answer.

$y=$.................because ......................

Work out the value of

i) $x,$

$x$=..........................[1]

ii) $y.$

$y=$...........................[1]

The diagram shows a triangle between two parallel lines, $AB$ and $CD$.

Find the value of

i) $v,$

$v$=............................. [1]

ii) $w,$

$w=$............................. [1]

iii) $y$.

$y$ = .............................  [1]

Complete the statements.

$a=$ ............................ because ............................   

$b=$ ........................... because ............................ 

Three regular polygons meet at a point.

One is a regular pentagon and another is a square.

Find the number of sides of the third polygon.

You must show your working.

The diagram shows a trapezium.

Work out the value of $x$.

$x$ = ..................................................

Kim knows that one angle of an isosceles triangle is 48°.
He says that one of the other angles must be 66°.

Explain why Kim is wrong.

The diagram shows triangle $PRS$ and a straight line $QS$. $Q$ is a point on $PR$.
Angle $QRS$ = 25°, angle $RSQ$ = 32° and $PS=QS$.

i) Find angle $PQS.$

Angle $PQS$ = ................................................... [2]

ii) Find angle $PSR$.

Angle $PSR$ = ................................................... [2]

The diagram shows a triangle.

Use the diagram to write down an equation and solve it to find the value of $x$.

$x$ = .................................. [4]

The diagram shows an isosceles triangle, $ABC$.
$BCD$ is a straight line.

Find the value of $x$.

$x=$ ................................ [2]

$ABCD$ is a rectangle.
$AE$ is parallel to $DBF$.

Find the value of $x$ and the value of $y$.

$x$ = ......................................................
$y$ = ................................................. .....

Two regular octagons and a square meet at point $P$.
Show, by calculation, that the three interior angles at $P$ add up to 360°.

The diagram shows two pairs of parallel lines.

Find the value of $a$, the value of $b$ and the value of $c$.

$$\begin{gathered} a=................................................. \\ b=................................................. \\ c=................................................. \end{gathered}$$

The diagram shows part of a different regular polygon.

$e$ is an exterior angle.
$i$ is an interior angle.
The ratio $e:i=2:13$.

i) Work out angle $e$.

[3]

ii) Work out the number of sides of this regular polygon.

[1]

$ABCDE$ is a pentagon.

Explain why the diagram shows that the sum of the interior angles of a pentagon is 540°.
Do not measure any angles.

In the diagram $AG$and $AF$ are straight lines.
Lines $BC$ and $DE$ are parallel.

Find angle $CED$ and give a reason for your answer.

Angle $CED$ = ................................. because ...................................

The diagram shows two regular pentagons.
Pentagon $FGHJK$ is an enlargement of pentagon $ABCDE$, centre $O$.

Find angle $AEK$.

Angle $AEK$ = .............................. 

In the diagram, $ABC$ is a straight line. $AD$ is parallel to $BE$, angle $BAD$ = 34° and $AB=BD.$

i) Complete the statements.

a) $p=$ ................ because ................................

[2]

b) $q=$ ................ because .................................

[2]

ii) Work out the value of $r$ and the value of $s$.

$r=$....................   
  $s=$ .................... [2]

iii) Find the value of t and give a reason for your answer.

$t=$................ because ........................

[2]

Each interior angle of a regular polygon is 162°.

Calculate the number of sides of the polygon.