It is given that $ riangle ABC \cong riangle PQR$, $AB = 5 ext{ cm}$, $\angle B = 40^\circ$, and $\angle A = 80^\circ$. Which of the following options is true?

Question

It is given that $	riangle ABC \cong 	riangle PQR$, $AB = 5 	ext{ cm}$, $\angle B = 40^\circ$, and $\angle A = 80^\circ$. Which of the following options is true?

Accepted Answer

**Solution:**

1. The sum of angles in a triangle is $180^\circ$. Given $\angle A = 80^\circ$ and $\angle B = 40^\circ$, calculate $\angle C$:

$$\angle A + \angle B + \angle C = 180^\circ$$
   $$80^\circ + 40^\circ + \angle C = 180^\circ$$
   $$120^\circ + \angle C = 180^\circ$$
   $$\angle C = 180^\circ - 120^\circ = 60^\circ$$

2. Since $	riangle ABC \cong 	riangle PQR$, corresponding sides and angles are equal:

- Side $AB$ corresponds to side $PQ$, so $PQ = AB = 5 	ext{ cm}$.
   - Angle $C$ corresponds to angle $R$, so $\angle R = \angle C = 60^\circ$.

**Answer:** $PQ = 5 	ext{ cm}$ and $\angle R = 60^\circ$

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