Question

ABC is a triangle with base BC and $\angle ABC={60}^{\circ }$.Through A, a straight line PQ is drawn parallel to BC . If $\angle QAC={55}^{\circ }$, Find the measure of $\angle BAC$ and $\angle ACB$.

• A. $\angle BAC={65}^{\circ }$ and $\angle ACB={55}^{\circ }$
• B. $\angle BAC={60}^{\circ }$ and $\angle ACB={60}^{\circ }$
  
• C. $\angle BAC={55}^{\circ }$ and $\angle ACB={65}^{\circ }$
• D. Insufficient Data

Answer 1

The correct option is A $\angle BAC={65}^{\circ }$ and $\angle ACB={55}^{\circ }$

Extend AB upside to point D

As PQ is parallel BC

$\Rightarrow \angle ABC=\angle DAQ$

$\Rightarrow \angle BAC=180-\angle QAC-\angle DAQ$

$\Rightarrow \angle BAC=180-55-60=65$

$\Rightarrow \angle ACB=180-60-65=55$