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

Question

In a quadrilateral ABCD, bisectors of angles A and B intersect at O such that &#x2220; AOB=75&#xB0;, then write the value of &#x2220; C+ &#x2220; D.

Philoid · Accepted Answer

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°