Question

Find the sum (in degrees) of ∠DCB and ∠CBE.

• A. 150

Answer 1

The correct option is A 150
Given: $\angle ADC={105}^{\circ }$

$\Rightarrow \angle ADC+\angle DCB={180}^{\circ }$
(Since adjacent angles are supplementary)

$\Rightarrow {105}^{\circ }+\angle DCB={180}^{\circ }$

$\Rightarrow \angle DCB={180}^{\circ }-{105}^{\circ }={75}^{\circ }$

AB || CD (opp. sides of a parallelogram)

$\Rightarrow \angle DCB=\angle CBE$
(Since alternate interior angles are equal)

$\Rightarrow \angle CBE={75}^{\circ }$

$\Rightarrow \angle DCB+\angle CBE={75}^{\circ }+{75}^{\circ }={150}^{\circ }$