Angles in Polygons & Parallel Lines (Cambridge International IGCSE Mathematics): 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 ............................

$AC$ and $DG$ are parallel lines.

The point $B$ lies on the line $AC$.

The points $E$ and $F$ lie on the line $DG$.

$BF=EF$.

Angle $CBF=52^{\circ}$.

Angle $BEF=x^{\circ}$.

NOT TO SCALE

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

$ABCD$ 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 model of a hall in the shape of a trapezium is made by joining together three equilateral triangles.

The perimeter of one of the triangles is 72 cm.

Work out the perimeter of the trapezium.

The trapezium model from part (a) is duplicated, with the copy being rotated and attached along the bottom of the original trapezium, making a regular polygon.

Give the name of this regular polygon.

Calculate the exterior angle, $x$, of the polygon in part (b).

Work out the interior angle, $y$,of the polygon in part (b).

In the diagram, $AI$ and $EH$ are straight lines.

Lines $BD$ and $FG$ are parallel.

Find the angle $DCG$.

Show that the sum of the interior angles in a hexagon is $720^{\circ}$.

Below are two regular shapes. Find angle $x$.