Question

In the figure, $AB$ is a chord parallel to $PR$ and $\angle BQR={70}^{\circ }$, find the measure of $\angle AQB$

• A. ${70}^{\circ }$
• B. ${30}^{\circ }$
• C. ${35}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is D ${40}^{\circ }$

m$\angle$BQR = 70° [Given].....(i)

$\angle BQR$ $\cong \angle BAQ$ ........ [Angles in alternate segments]

$\therefore$ $m\angle BQR$ $=m\angle BAQ={70}^o$ ...(ii)

Chord $AB\parallel PR$,

On transversal $AQ,$

$\angle BAQ$ $\cong \angle AQP$ ....... [Alternate angles]

$\therefore$ $m\angle BAQ$$=m\angle AQP={70}^o$ ....... [From (ii)]

$m\angle AQP+$ $m\angle AQB+$$m\angle BQR={180}^o$ .... [Angles in a straight line]

$70+m\angle AQB+70=180$

$\therefore$$m\angle$$AQB=180-140$

$\therefore$ $m\angle$$AQB={40}^o$