Question

Assertion: In the figure ∠A = 2x, ∠B = 3x, ∠E = 75° and CD || EF. ∴ x = 15°.

Reason: Co-interior ∠S of || lines are equal.

Options

• Both A and R are true and R is the correct reason for A.

• Both A and Rare true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

A is true but R is false.

Explanation:

In triangle ABC,

2x + 3x + ∠C = 180°

⇒ ∠C = 180° – 5x

Since CD || EF and CE is a transversal, ∠C and given ∠E = 75° are co‑interior.

So, they are supplementary: 

∠C + 75° = 180°

⇒ ∠C = 105°

Thus, 180° – 5x = 105°

⇒ 5x = 75°

⇒ x = 15°

So, the assertion is true. 

However, the Reason is wrong: co‑interior angles on parallel lines are supplementary sum to 180°, not equal.