Angles in Polygons & Parallel Lines (Cambridge (CIE) O Level Maths): Exam Questions

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 $x$.

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

The diagram shows a hexagon.

Write an equation and solve it to find the value of $x$.

The diagram shows an octagon.

Write an equation and solve it to find the value of $x$.

$AC$ 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.

[3]

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

[2]

$ABCD$ is a parallelogram.

Angle $ADB=38°$.
Angle $BEC=41°$.
Angle $DAB=120°$.

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  $3a+5b=170$.

[1]

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

[1]

iii) Solve these simultaneous equations.

Show all your working.

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

iv) Find the size of the smallest angle in the triangle. [1]

Show that each interior angle of a regular pentagon is $108°$. 

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 $x=y$.