Applying the properties of shapes to determine an angle test questions

1

This triangle is isosceles. What is the value of h?

Diagram of isosceles triangle with a 65° angle and h° angle to find

\[50^\circ\]

\[65^\circ\]

\[130^\circ\]

2

For this kite what is the value of k?

Diagram of kite with a 77° angle and k° angle to find

\[13^\circ\]

\[77^\circ\]

\[90^\circ\]

3

Calculate the size of angle \(x^\circ\) from the diagram.

Diagram of triangle with 50° angle x° angle to find

\[65^\circ\]

\[50^\circ\]

\[130^\circ\]

4

Calculate the size of angle \(x^\circ\) from the diagram.

Diagram of triangle with 113° angle outside and x° angle to find

\[67^\circ\]

\[46^\circ\]

\[134^\circ\]

5

Calculate the length of the radius x mm from the diagram.

Give your answer correct to the nearest mm.

Diagram of triangle with right-angle inside and values 240mm and 130 mm

50mm

273mm

177mm

6

Calculate the size of angle \(x^\circ\) from the diagram.

Diagram of right-angled triangle with 27° angle and x° angle to find

\[27^\circ\]

\[54^\circ\]

\[63^\circ\]

7

In the diagram below, PQ is the diameter of the circle.

Calculate the size of angle \(x^\circ\).

Diagram of triangle with 65° angle with x° angle to find

\[25^\circ\]

\[90^\circ\]

\[65^\circ\]

8

AB is the diameter of the circle.

Calculate the length of AC.Give your answer correct to one decimal place.

Diagram of triangle with 8cm and 4cm values

48.0cm

8.9cm

6.9cm

9

In the diagram below, PT is the tangent and CT is the radius of the circle.

Calculate the size of angle \(y^\circ\).

Diagram of right-angled triangle with 58° angle and y° angle to find

\[16^\circ\]

\[32^\circ\]

\[58^\circ\]

10

TY is a tangent and XY is the diameter of the circle.

Calculate the length of the tangent TY.

Give your answer correct to one decimal place.

Diagram of triangle with 12cm and 10cm values

6.6cm

15.6cm

10.9cm