Question

If $\angle AMQ$ = $\angle AMP={100}^{\circ }$ and $\angle Q={50}^{\circ }$, find the measure of $\angle PAM$.

• A. 60${}^{\circ }$
• B. 50${}^{\circ }$
• C. 30${}^{\circ }$
• D. 40${}^{\circ }$

Answer 1

The correct option is C 30${}^{\circ }$

In $△AMP$ and $△AMQ$,
AM = AM .... (Common side)
$\angle AMP=\angle AMQ$ ....(Given)
$MP=MQ$.... (Given)

Therefore, $△AMP\cong △AMQ$ by SAS criterion for congruency of triangles.

$\angle$MPA = $\angle$MQA = 50${}^{\circ }$ .... (corresponding parts of congruent triangle)

We know that, the sum of all internal angles of a triangle is 180°.
$\therefore \angle$PAM = 180${}^{\circ }$ - ($\angle$AMP + $\angle$MPA)
$\Rightarrow \angle$PAM = 180${}^{\circ }$ - (100${}^{\circ }$ + 50${}^{\circ }$) = 30${}^{\circ }$