Question

In the given figure, if $PQ\parallel RS,\angle PAB={70}^{\circ }$ and $\angle ACS={110}^{\circ }$, find the measure of $\angle BAC$

• A. ${40}^{\circ }$
• B. ${70}^{\circ }$
• C. ${110}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

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

Given

$PQ\parallel RS$

$\angle PAB={70}^0$

$\angle ACS={110}^0$

$\angle BAC=?$

$\angle BCS=180-110={70}^0$ (straight line)

$\angle DAB=\angle ABC={70}^0$ (alternate angle)

Now from $△ABC$

By angle sum property

$\angle BAC+70+70={180}^0$

$\angle BAC={40}^0$