In $$\triangle$$​ABC, ∠A = 85° and ∠C= 58°. If ∆PQR is similar to ∆ABC, and in correspondence, then find ∠Q.

Correct option is A

Given:
In triangle ABC, ∠A = 85° and ∠C = 58°.
Triangle PQR is similar to triangle ABC in correspondence. We are required to find ∠Q.
Formula Used:
According to the property of similar triangles, the corresponding angles of similar triangles are equal. Therefore, if ∆PQR is similar to ∆ABC, then:
∠P = ∠A, ∠Q = ∠B, and ∠R = ∠C
We know that the sum of the angles in any triangle is 180°.
Thus, in triangle ABC: ∠A + ∠B + ∠C = 180°
Solution:
We are given ∠A = 85° and ∠C = 58°.
Using the angle sum property:
∠B = 180° - (∠A + ∠C)
∠B = 180° - (85° + 58°)
∠B = 180° - 143° = 37°
 Since triangle PQR is similar to triangle ABC, the corresponding angle ∠Q = ∠B.
Thus, ∠Q = 37°.
Therefore, the value of ∠Q is 37°.