Two similar triangles are given i.e. LMN ~ PQR, with measurement of angle and side as ∠L = 40°, ∠N = 80°, LM = 6 cm, LN = 5 cm, and PQ = 7.5 cm. Find the value of ∠Q and side PR, respectively.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 60°, 10 cm.
△LMN ~ △PQR
LM/PQ = LN/PR
6/7.5 = 8/PR
PR = (8 × 7.5)/6 = 10 cm
The sum of all angles in a triangle is 180°
In △LMN, ∠L + ∠M + ∠N = 180°
⇒ 40° + ∠M + 80° = 180°
⇒ ∠M = 180° - 120° = 60°
Since △LMN ~ △PQR, the corresponding angles are equal: ∠M = ∠Q = 60°
Hence, the measure of angle Q is 60°, and the length of side PR is 10 cm.