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

Calculate the size of one interior angle of a regular polygon with 40 sides.

Find the interior angle of a regular polygon with 24 sides.

In the diagram, AC and BD are straight lines.

Find the value of $p$ and the value of $q$.

$p$ = ...................................................

$q$ = ...................................................

The interior angle of a regular polygon with $n$ sides is 150°.

Calculate the value of $n$.

$n=$................................................

A regular polygon has 72 sides.

Find the size of an interior angle.

The diagram shows two parallel lines PAQ and SBCT.

AB = AC and angle QAC = 43°.

Find the value of $x$.

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

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

Lines $BD$ and $FG$ are parallel.

Find the angle $DCG$.

$AC$ is parallel to $FBD$, $ABC$ is an isosceles triangle and $CBE$ is a straight line.

Find the value of $x$.

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

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

Find angle $AEK$.

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

The area of pentagon $FGHJK$ is $73.5\text{cm}^{2}$. The area of pentagon $ABCDE$ is $6\text{cm}^{2}$.

Find the ratio perimeter of pentagon $FGHJK$ : perimeter of pentagon $ABCDE$ in its simplest form.

......................... : .........................

In a regular polygon, the interior angle is 11 times the exterior angle.

i) Work out the number of sides of this polygon.

ii) Find the sum of the interior angles of this polygon.

$ABCD$ is a parallelogram.

Angle $ADB=38^{\circ}$. Angle $BEC=41^{\circ}$. Angle $DAB=120^{\circ}$.

Calculate the size of angle $x$. You must give reasons for your answer.

The diagram shows a triangle and a quadrilateral. All angles are in degrees.

i) For the triangle, show that $3a+5b=170$.

ii) For the quadrilateral, show that $9a+7b=310$.

iii) Solve these simultaneous equations. Show all your working.

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

$b$ = ................................................... [3]

iv) Find the size of the smallest angle in the triangle.

Show that each interior angle of a regular pentagon is $108^{\circ}$.

The diagram shows a regular pentagon $ABCDE$. The vertices of the pentagon lie on a circle, centre $O$, radius $12\text{cm}$. $M$ is the midpoint of $BC$.

i) Find $BM$.

$BM$ = ........................................ cm [3]

$OMX$ and $ABX$ are straight lines.

iia) Find $BX$.

$BX$ = ........................................ cm [3]

iib) Calculate the area of triangle $AOX$.

........................................ cm² [3]

The diagram shows a regular 10-sided polygon, $ABCDEFGHIJ$

Show that $x=y$.