Question

$\text{In the given figure ABCO is a parallelogram.}\text{AB, CD and OD are equal in length.}\text{If}\angle BAO={110}^{\circ },\text{then find the measure}\text{of}\angle BCD.$

• A. ${150}^{\circ }$
• B. ${160}^{\circ }$
• C. ${170}^{\circ }$
• D. ${180}^{\circ }$

Answer 1

The correct option is C ${170}^{\circ }$

$\text{Given:}\angle BAO={110}^{\circ }$

$\therefore \angle BAO=\angle BCO={110}^{\circ }\text{[Opposite angles of a parallelogram}\text{are equal]}$

$AB=CO\text{[Opposite sides of a parallelogram are}\text{equal]}$

$\Rightarrow OC=CD=OD$

$\Rightarrow △OCD\text{is a equilateral triangle}$
$\text{and}\angle OCD={60}^{\circ }.$

$\angle BCD=\angle BCO+\angle OCD$
$\Rightarrow \angle BCD={110}^{\circ }+{60}^{\circ }$
$\Rightarrow \angle BCD={170}^{\circ }$