Question

What is the sum of the measures of the angles ∠A, ∠B, ∠C, ∠D, ∠E, and ∠F in the given figure?

• (A) 180°
• (B) 360°
• (C) 540°
• (D) 720°

Answer 1

The Correct Option is B

Explanation:
Given:

Calculation:As, the given figure is

Here, in Δ LMN, ∠1 + ∠ 2 + ∠ 3 = 180°    ----(i) (Sum of interior angles of a triangle = 180°)As, ∠BLM is the exterior angle for Δ ABL,So, ∠A + ∠B = (∠BLM Sum of two interior angle is equal to the exterior angle)⇒ ∠A + ∠B = 180° - ∠1      ----(ii)Similarly, ∠CML and ∠FNL are the exterior angles of Δ CDM and Δ FEN,So, ∠C+ ∠D = 180° - ∠2      ----(iii)And, ∠E + ∠F = 180° - ∠3      ----(iv)Adding equations (ii), (iii) and (iv) we get∠ A + ∠B + ∠C + ∠D + ∠E + ∠F = 180° × 3 - (∠1 + ∠2 + ∠3)   ----(v)From (i) and (v), we get∠A + ∠B + ∠C + ∠D + ∠E + ∠F  = 180° × 3 - 180°⇒ ∠A + ∠B + ∠C + ∠D + ∠E + ∠F  = 360°∴  The sum of the measures of the angles ∠A, ∠B, ∠C, ∠D, ∠E, and ∠F in the given figure is 360°.Hence, the correct option is (B).