Basic Angle Properties (Cambridge International IGCSE Maths): Exam Questions

Triangle $ABC$ is isosceles. Angle $ABC$ = 32° and $AB=AC$.

Find angle $BAC$.

Angle $BAC$ = .................................................

Work out the value of$x$. Give a geometrical reason for your answer.

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

A student measures the angles in a triangle as 55°, 85° and 50°.

Explain why the student is incorrect.

The diagram shows an isosceles triangle.

Find the value of $x$.

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

$ABC$ is a straight line.

Find the value of $y$.

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

The diagram shows an isosceles triangle and a straight line. Work out the value of $w$.

$w=$...............................[2]

Work out the value of $w.$ Give reasons for your answer.

$w=$ ............................ because ....................................................................................................

$QRS$is an isosceles triangle and $PQR$ is a straight line.

Find the value of $z$.

$z$ = ...................................................

$ABC$ is an isosceles triangle. $BCD$ is a straight line.

Find the value of $a$.

$a$ = ..............................................

$ABC$is a straight line and $BCD$ is an isosceles triangle. Find the value of$x$.

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

In the triangle $ABC,AB=AC$ and angle $BAC=38^{\circ}$.

$BCD$is a straight line.

Work out angle $ACD$.

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

A triangle is isosceles. One of its angles is 96°.

Find the other two angles.

........................ and ........................

Find the value of $x$.

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

The diagram shows a trapezium.

Work out the value of $x$.

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

Kim knows that one angle of an isosceles triangle is 48°. He says that one of the other angles must be 66°.

Explain why Kim is wrong.

The diagram shows triangle $PRS$ and a straight line $QS$. $Q$ is a point on $PR$. Angle $QRS$ = 25°, angle $RSQ$ = 32° and $PS=QS$.

i) Find angle $PQS.$

Angle $PQS$ = ................................................... [2]

ii)Find angle $PSR$.

Angle $PSR$ = ................................................... [2]

The diagram shows a triangle.

Use the diagram to write down an equation and solve it to find the value of $x$.

$x$ = .................................. [4]

The diagram shows an isosceles triangle, $ABC$. $BCD$ is a straight line.

Find the value of $x$.

$x=$ ................................ [2]