Question

In $\Delta PQR,m\angle P={50}^o$ and the external bisectors of $\angle Q$ and $\angle R$ meet in O, then the measure of $\angle QOR$ is:

• A. ${65}^o$
• B. ${70}^o$
• C. ${75}^o$
• D. ${80}^o$

Answer 1

The correct option is A ${65}^o$

Given $\angle P=50°$

By angle sum property

$\angle P+\angle Q+\angle R=180°$

$\angle P+2(\angle OQR+\angle ORQ)=180°$

$P+2[180-\angle QOR]=180$

$2[180-\angle QOR]=130$

$180-\angle QOR=65$

$\angle ROQ=115°$ [interior angle]

$\angle QOR=180-115-65°$ [exterior angle]