Question

In the adjacent figure, if $\angle AOC={110}^0$, then the value of $\angle Dand\angle B$ respectively.

• A. ${55}^0,{125}^0$
• B. ${55}^0,{110}^0$
• C. ${110}^0,{25}^0$
• D. ${125}^0,{55}^0$

Answer 1

The correct option is A ${55}^0,{125}^0$

Given, $\angle AOC={110}^0$
Also, we know $\angle AOC=2\angle ADC$ (angle subtended by an arc at the center is double the angle subtended by it at any point on the circumference)
$\therefore \angle ADC={55}^0$

Also, $\angle B+\angle D={180}^0$ (ABCD is a cyclic quadrilateral and opposite angles of it are supplementary)
$⟹\angle B={125}^0$