Question

Assertion (A): ΔАВС ~ ΔРQR such that ∠A = 65°, ∠C = 60°. Hence ∠Q = 55°. 

Reason (R): Sum of all angles of a triangle is 180°.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true, but Reason (R) is not correct explanation for Assertion (A).

• Assertion (A) is true, but Reason (R) is false.

• Assertion (A) is false, but Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true, but Reason (R) is not correct explanation for Assertion (A).

Explanation:

Given, ΔАВС ~ ΔРQR

∠A = 65°, ∠C = 60°

By angle sum property of a triangle,

∠A + ∠B + ∠C = 180°

65° + ∠B + 60° = 180°

∠B = 180° – 125°

∠B =  55°

Since △ABC∼△PQR, corresponding angles are equal.

∠B = ∠Q = 55°

Reason (R) gives only the measure of ∠B using angle sum property, but the conclusion ∠Q = 55° is obtained using the property of similar triangles that corresponding angles are equal. Since this property is not stated in Reason (R), it is not the correct explanation of Assertion (A).