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

Work out the size of one interior angle of a regular 16-sided polygon.

Work out the size of one interior angle of a regular 9-sided polygon.

i) Write down the mathematical name for an 8-sided polygon.

ii) Work out the size of an interior angle of a regular 24-sided polygon.

Find the size of one interior angle of a regular octagon.

The diagram shows two parallel lines and a straight line crossing them.

Write down, using letters from $a$ to $g$,

the angle that is alternate to angle $X$,

Extract:

The diagram shows two parallel lines and a straight line crossing them. Write down, using letters from a to g, the angle that is alternate to angle X.

the angle that is corresponding to angle $X$.

Find the size of one interior angle of a regular 10-sided polygon.

Work out the size of one interior angle of a regular polygon with 20 sides.

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

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

$x=..............................\,y=..............................$

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 ....................................

Extract:

In the diagram, AB is parallel to CD.

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 $a$.

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 $c$.

$a=.................................................\,b=.................................................\,c=.................................................$

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 $e$.

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

$ABCDE$ 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 ................................

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

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 ........................

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.