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

The diagram shows two triangles, $ABD$ and $ADC$.

$BDC$ is a straight line, $AB=AC$ , angle $ABD=61°$ and angle $ADC=81°$.
Work out angle $DAC$.

Angle $DAC$ = .................................

Find the number of sides of a regular polygon with interior angle 162°.

The interior angle of a regular polygon with $n$ sides is $156°$.

Work out the value of $n$.

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

The diagram shows triangle ABC.
The triangle is reflected in the line BC to give a quadrilateral ABDC.

Write down the mathematical name of the quadrilateral ABDC.

Find angle ACD.  

Angle ACD = ................................................

$AB=BC$ and $ABD$ is a straight line.  

Find the value of $x$.  

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

A regular polygon has an interior angle of 176°.

Find the number of sides of this polygon.

The exterior angle of a regular polygon is $x$° and the interior angle is $8x$°.

Calculate the number of sides of the polygon.

Complete the statements.

a = ............................................... because ............................................... 
b = ............................................... because ...............................................     

The diagram shows a regular octagon and a regular hexagon.

Find the size of the angle marked $x$.
You must show all your working.

The diagram shows quadrilateral $ABCD$ with $AD$ extended to $E$. Angle $BCD=135°$, angle $BAD=83°$ and angle $CDE=122°$.

Find the value of $x$.

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

ABDF is a parallelogram and BCDE  is a straight line.
AF = 12cm, AB = 9 cm, angle CFD = 40° and angle FDE = 80°.

Explain why triangle CDF  is isosceles. 

PQR is a triangle.
T is a point on PR and U is a point on PQ.
RQ is parallel to TU.

Explain why triangle PQR is similar to triangle PUT.
Give a reason for each statement you make.

The diagram shows a trapezium.

Work out the value of $x$.

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

A hexagon has five angles that each measure 115°.

Calculate the size of the sixth angle.

The angles of a quadrilateral are $x°$, $(x+5)°$, $(2x-25)°$ and $(x+10)°$.

Find the value of $x$.

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

The diagram shows an isosceles triangle ABC with AB = AC. LCM and BCN are straight lines and LCM is parallel to AB.
Angle ACL = 56°.  

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

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

The diagram shows a regular pentagon.
$AB$ and $CD$ are two of the lines of symmetry of the pentagon.

Work out the size of the angle marked $x$.
You must show all your working.

$ABCDEFGHI$ is a regular 9-sided polygon.

The vertices $B$ and $E$ are joined with a straight line.

Work out the size of angle $BEF$. You must show how you get your answer.

$PQRST$ is a regular pentagon.
$R,U$ and $T$ are points on a circle, centre $O$.
$QR$ and $PT$ are tangents to the circle.
$RSU$ is a straight line.

Prove that $ST=UT$.