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

$ABC$ is parallel to $DEFG$ $BC=BF$ Angle $ABE=39^{\circ}$ Angle $CFG=63^{\circ}$

Work out the size of angle $x$. Give a reason for each stage in your working.

The diagram shows two congruent regular pentagons drawn inside a regular octagon.

One side of each pentagon lies along a side of the octagon.

$AB$ is a side of the octagon. $AC$ is a side of one of the pentagons. $BC$ is a side of the other pentagon.

Work out the size of angle $y$. Show your working clearly

Here is a 9-sided regular polygon $ABCDEFGHJ$, with centre $O$

$ODK$ and $FEK$are straight lines.

Work out the value of $x$

The diagram shows two triangles $ABE$ and $ECD$

Triangle $ABE$ is isosceles with $AE=EB$ $ADE$ and $EBC$ are straight lines.

Angle $CDE=42^{\circ}$ The reflex angle $ECD=296^{\circ}$ Angle $BAE=x^{\circ}$

Work out the value of $x$

$ABCD$and $EFGH$are straight lines. $KFBJ$and $MGCL$are parallel straight lines.

$\mathrm{angle}ABJ=125^{\circ}\mathrm{angle}BFG=32^{\circ}\mathrm{angle}FGM=x^{\circ}\mathrm{angle}LCD=y^{\circ}$

Write down the value of $x$

(i) Work out the value of $y$

(ii) Give a reason for your answer to (b) (i)

The diagram below shows a triangle $PRQ$ and straight line $PQS$. The diagram is not drawn to scale.

• Angle $P R Q = ( 8 x + 2 )^{\circ}$
• Angle $Q P R = ( 11 x + 10 )^{\circ}$
• Angle $R Q S = ( 15 x + 32 )^{\circ}$

Find the value of $x$