Question : In the given figure, the measure of $\angle A$ is:
Option 1: $50^{\circ}$
Option 2: $40^{\circ}$
Option 3: $20^{\circ}$
Option 4: $60^{\circ}$
Correct Answer: $40^{\circ}$
Solution : According to the Side Angle Side (SAS) congruency axiom, two triangles are congruent if their respective included angles and the corresponding two sides are equal.
In $\triangle ABC$ and $\triangle PQR$,
AB = PQ = 7 cm
$\angle B= \angle Q=70^{\circ}$
BC = QR = 8 cm
By SAS rule, $\triangle ABC\cong \triangle PQR$.
⇒ $\angle A =\angle P$
⇒ $2x=x+20^{\circ}$
⇒ $2x–x=20^{\circ}$
⇒ $x=20^{\circ}$
The measure of $\angle A=2x=2\times 20^{\circ}=40^{\circ}$.
Hence, the correct answer is $40^{\circ}$.
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