Angles in Polygons & Parallel Lines (Cambridge (CIE) IGCSE International Maths: Core): Exam Questions

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 ............................ 

Work out the value of $a$.

[1]

Work out the value of $b$.

$ABCD$ 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.

A regular polygon has $n$ sides.

Find an expression in terms of $n$ for the size of one interior angle of the polygon.