Question

In the given figure, 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° and ∠CDE=110

a)Find the measure of ∠BAC

b) What can you say for ∠ BAC and ∠ BDC?

Answer 1

Answer:

angle BEC+DEC=180° (straight line)

DEC=180°-130°

DEC=50°

DEC+DCE+EDC=180°(sum of angles in a triangle is 180°)

50°+20°+EDC=180°

70°+EDC=180°

EDC=180°-70°

EDC=110°

EDC=BAC( angle of triangles drawn from common base to a cricle are equal)

BAC=110°