iGCSE Mathematics (0580) :C4.7 Calculate unknown angles using the following geometrical properties. iGCSE Style Questions Paper 3

Question



A, B, C and D are points on the circumference of a circle, centre O.
EF is a tangent to the circle at A.
GH is a straight line through the point A.
Angle CBD = 24° and angle OAG = 78°.
(a) (i) Write down the mathematical names of lines BC and OA.
(ii) Find the value of x, giving a reason for your answer.
(iii) Find the value of y, giving a reason for your answer.
(b) The diagram shows a regular polygon, centre O.

(i) Write down the name of this polygon.
(ii) Find the value of w.
Show all your working.
(c) The exterior angle of another regular polygon is 24°.
Calculate the number of sides this polygon has.

Answer/Explanation

Answer:

(a) (i) Chord
Radius
(ii) 12
Tangent [meets] radius [at] 90 [°]
(iii) 66
Angles [in] triangle 180 or
Angle [in a] semi–circle [= 90]

(b) (i) Octagon
(ii) \(360 \div [=45]\)
(180 – their 45) ÷ 2
67.5

(c) 15

Question

(a)

AB is a straight line.
Find the value of p.
(b)

Find the value of q.
(c)

DCB is a straight line and AB = AC.
Find the values of r and s.
(d)

The straight line AB crosses two parallel lines.
Find the value of t.
(e)

A and B lie on a circle, centre O.
AC and BC are tangents to the circle.
Find the value of u.

Answer/Explanation

Answer:

(a) 29
(b) 42
(c) [r =] 66 and [s =] 114
(d) 50
(e) 56

Question

(a) A cuboid measures 6cm by 3cm by 2cm.
(i) On this 1 \(cm^2\) grid, complete the net of the cuboid.

(ii) Calculate the volume of the cuboid.
……………………………. \(cm^3\)
(b)

Write down the mathematical name of this shape.
(c)

Mark an obtuse angle on this trapezium.
(d) A regular polygon has an exterior angle of 22.5°.
Work out how many sides this polygon has.
(e)

The diagram shows a shape made from a semi-circle, radius 6cm, and a right-angled triangle.
(i) Show that x = 16.
(ii) Calculate the area of the shape.
…………………………… \(cm^2\)

Answer/Explanation

Answer:

(a) (i) Correct net
(ii) 36

(b) Hexagon

(c) Obtuse angel indicated

(d) 16

(e) (i) \(\sqrt{20^2 – 12^2}\)
(ii) 153 or 152.5 to 152.6

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