In Fig. 10.39, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠ BEC = 130° and ∠ ECD = 20°. Find∠ BAC.

Question

In Fig. 10.39, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that &#x2220; BEC = 130&#xB0; and &#x2220; ECD = 20&#xB0;. Find &#x2220; BAC.

Philoid · Accepted Answer

In ΔCDE,

∠CDE + ∠DCE = CEB (Exterior angle)

∠CDE + 20° = 130°

∠CDE = 110°

However, ∠BAC = ∠CDE (Angles in the same segment of a circle)

∠BAC = 110°