Question

Find the value of $\angle$ DCE:

• A. 100°
• B. 80°
• C. 90°
• D. 75°

Answer 1

The correct option is B

80°

$\angle$ BAD = $\frac{1}{2}$ BOD

$\angle$ BAD = $\frac{1}{2}$( ${160}^{\circ }$)

$\angle$ BAD = ${80}^{\circ }$

ABCD is a cyclic quadrilateral

$\angle$ BAD + $\angle$ BCD = ${180}^{\circ }$

$\angle$ BCD = ${100}^{\circ }$

$\angle$ DCE = ${180}^{\circ }$ - $\angle$ BCD

$\angle$ DCE = ${180}^{\circ }$ – ${100}^{\circ }$

$\angle$ DCE = ${80}^{\circ }$