Angles

The oil-rigs sit at the four vertices of rectangle $ABCD$. The bearing of $B$ from $A$ is $040^\circ$.

May/June 2015

From the diagram, $AB$, $BC$, $CD$ and $DE$ form four consecutive sides of a regular polygon. The polygon has each interior angle equal to $160^\circ$. $ABPQR$, $DCP$ and $EDQ$ are straight lines.

May/June 2016

The diagram shows that the bearing of $B$ from $A$ is $170\degree$. The bearing of $A$ from $C$ is $060\degree$. The bearing of $C$ from $B$ is $x\degree$.

May/June 2016

The diagram shows $AB$ parallel to $DC$, while $AC$ and $BD$ meet at $E$. Triangle $ADE$ is right-angled and isosceles, with $AD = DE$. $\angle ABD = 25^\circ$.

May/June 2017

The diagram shows $AB$ parallel to $DE$. $\angle ABC = 114^\circ$ and $\angle CDE = 143^\circ$.

May/June 2017

In a pentagon, four of the angles are $2x^\circ$ and the remaining angle is $x^\circ$. Calculate the value of $x$.

May/June 2017

The diagram illustrates where the two villages $A$ and $B$ are located.

May/June 2017

A $22$-sided irregular polygon is given. Calculate the combined measure of all its interior angles.

May/June 2018

PBQ and RACS lie parallel to each other. BAE and BCD each form straight lines. $AB = AC$, $\angle QBC = 58^\circ$ and $\angle AED = 47^\circ$.

May/June 2019

The diagram illustrates quadrilateral $ABCD$, with $AD$ extended to $E$. The angles given are $\angle BCD = 135^\circ$, $\angle BAD = 83^\circ$ and $\angle CDE = 122^\circ$.

May/June 2021

The diagram depicts a pentagon.

May/June 2022

The diagram depicts four straight lines intersecting at one point.

May/June 2023

The figure shows equilateral triangle $B$ together with part of regular polygon $A$, and they share one side. The interior angle of polygon $A$ is $165^\f$.

May/June 2023

A square and a regular pentagon are attached along a single shared edge, as the diagram indicates.

May/June 2024

AEC and BED lie on straight lines. $ED = EC$.

May/June 2025

The diagrams are not drawn to scale.

May/June 2025

A sketch showing three parallel lines crossed by transversals is given (not to scale).

May/June 2025

Calculate the measure of the interior angle of a regular octagon.

May/June 2025

For a regular polygon, each interior angle is $171^\circ$. Determine how many sides the polygon has.

Oct/Nov 2016

From the diagram, $ABC$ lies on one straight line, and $BF$ is parallel to $DE$. Also, $\angle FBA = 74^\circ$ and $\angle DBF = 65^\circ$.

Oct/Nov 2016

Within the diagram, $ABCD$ forms a parallelogram. $P$ and $Q$ lie on $AB$ and $BC$ respectively, with $PB = BQ$ and $DPQ = 90^\circ$. $BPQ = a^\circ$.

Oct/Nov 2016

From the diagram, $ABC$ runs parallel to $DEFG$. Also, $BC = BE$, $\angle ACE = 35^\circ$ and $\angle BFG = 102^\circ$.

Oct/Nov 2017

Within the diagram, $AFGB$, $BGDC$ and $FEDG$ are parallelograms. When extended, $EF$ and $BA$ meet at $H$. $\angle BGF = 130^{\circ}$ and $\angle DGF = 120^{\circ}$.

Oct/Nov 2018

Each interior angle of a regular polygon measures $175^\circ$. Find how many sides the polygon has.

Oct/Nov 2018

A polygon with $12$ sides is given. Calculate the sum of its interior angles.

Oct/Nov 2019

In the diagram, $AP$, $BQ$ and $CR$ bisect the angles of triangle $ABC$. These bisectors meet at $O$. $\angle OBP = 31^\circ$, $\angle OCQ = 22^\circ$ and $\angle OAQ = 37^\circ$.

Oct/Nov 2019

In the diagram, $ABC$ and $DEF$ lie on parallel lines. $\angle ABE = 123^{\circ}$ and $\angle CEF = 40^{\circ}$.

Oct/Nov 2020

Within the diagram, both $OC$ and $OA$ make angles of $70^{\circ}$ with the North line. $\angle AOB = x^{\circ}$ and $\angle BOC = y^{\circ}$.

Oct/Nov 2020

The clock shown in the diagram reads $2.30\,\text{pm}$.

Oct/Nov 2020

One angle in a triangle measures $55^\circ$. The remaining two angles are in the ratio $3:2$.

Oct/Nov 2021

A regular polygon has an interior angle of $156^\circ$.

Oct/Nov 2021

In the diagram, $ABCD$ and $EFGH$ are parallel lines. The lines $CF$ and $BG$ cross at $X$. $\angle CFG = 53^\circ$, $\angle BGF = 46^\circ$ and $\angle BXC = 81^\circ$.

Oct/Nov 2021

Calculate angle $PRQ$.

Oct/Nov 2021

The diagram shows that $AD$, $AB$ and $BC$ are three edges of a regular pentagon, while $DC$ is one diagonal of that pentagon. Also, $AB$ is parallel to $DC$.

Oct/Nov 2022

$ABC$ is an isosceles triangle, with $AB = BC$. The ratio $\angle ABC : \angle BAC = 2 : 5$.

Oct/Nov 2022

A pentagon has exterior angles of $150^\circ$, $100^\circ$, $45^\circ$ and $35^\circ$. Calculate the size of the missing exterior angle.

Oct/Nov 2023

The diagram depicts one straight line intersecting two parallel lines.

Oct/Nov 2023

$AB$ and $CD$ are parallel. $EC$ and $FB$ are also parallel. Angle $ABF = 73^{\circ}$.

Oct/Nov 2023

A regular polygon has an interior angle of $160^{\circ}$.

Oct/Nov 2024

Five straight lines are drawn in the diagram: three are horizontal and parallel, while the other two are sloping and parallel. The angles shown are $112^\circ$, $p^\circ$ and $q^\circ$.

Oct/Nov 2025

The diagram depicts an isosceles triangle whose apex angle is $56^\circ$.

Oct/Nov 2025

The diagram displays a regular pentagon and a regular hexagon attached along one side.

Oct/Nov 2025