Question

The diagram above shows

circle ABCD
with Centre E Quadrilateral EADC is a rhombus.
<BAE =<ECB=n and <ABC=m.
find
i) m
ii) n​

Answer 1

• m = 60°
• n = 30°

Explanation:

Opposite angles D and E in the rhombus are congruent. The measure of arc ADC is the same as the measure of central angle AEC. The measure of arc ABC is twice the measure of angle AEC, so the measure of arc ABC is twice the measure of arc ADC.

This means that short arcs AB, BC and CA are all 120°. Inscribed angle ABC (angle m) is half that value, or 60°.

Likewise, the angle BAC is 60°. We know that angle EAD is supplementary to angle AEC, so is 180° -120° = 60°. Segment AC bisects this angle, so angle n is 60°/2 = 30° less than angle BAC.

angle m is 60°, angle n is 30°