Question

In a quadrilateral ABCD, bisectors of angles A and B intersect at O such that ∠AOB = 75°, then write the value of ∠C+∠D.

Answer 1

Given,

In quadrilateral ABCD,

∠x+∠y+75° = 180° 

(angle sum property of triangle) 

= ∠x +∠y = 180°- 75° = 105° 

=2(∠x +∠y) = 2 × 105° = 210° 

∴ ∠C +∠D = 360°- 210° = 150°