In ΔABC, ∠A = 85° and ∠C = 58°. If ΔPQR is similar to ΔABC, and in correspondence, then find ∠Q.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 37°.
Given that
In ΔABC, ∠A = 85° and ∠C = 58°
If ΔPQR is similar to ΔABC,
The corresponding angles are the same as two similar triangles
According to the question
So, ∠A = ∠P = 85° and ∠C = ∠R = 58°
As we know,
⇒ ∠P + ∠Q + ∠R = 180°
⇒ 85° + ∠Q + 58° = 180°
⇒ ∠Q = 180° - 143° = 37°