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

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 $CDE=42°$
The reflex angle $ECD=296°$
Angle $BAE=x°$

Work out the value of $x$

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

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

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 $PRQ=\left(8x+2\right)°$

• Angle $QPR=\left(11x+10\right)°$

• Angle $RQS=\left(15x+32\right)°$

Find the value of $x$