iGCSE Mathematics (0580) :E4.7 Calculate unknown angles using the following geometrical properties:iGCSE Style Questions Paper 2

Question

The diagram shows a circle and eight chords.

Calculate the values of \( u \), \( v \), \( w \) and \( x \).

▶️ Answer/Explanation

Solution

Ans: \( u = 20 \), \( v = 52 \), \( w = 108 \), \( x = 36 \)

1. \( u = 20° \) (given angle)

2. \( v = 180 – 72 – 56 = 52° \) (angles in triangle)

3. \( w = 180 – 72 = 108° \) (angles on straight line)

4. \( x = 180 – 108 – 36 = 36° \) (angles in triangle)

Question

A, B, C and D are points on a circle.
TU is a tangent to the circle at D.
DA is parallel to CB.

Find the value of x and the value of y.

▶️ Answer/Explanation

Solution

Ans: x = 38, y = 22

1. x = angle between tangent and chord = angle in alternate segment (38°)

2. Since DA ∥ CB, angle CBA = 180° – 38° = 142°

3. In triangle ABC: y = 180° – 38° – 120° = 22°

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