Question

In the given figure, side BC of ∆ABC has been produced to a point D. If ∠A = 3y°, ∠B = x°, ∠C = 5y° and ∠CBD = 7y°. Then, the value of x is

(a) 60
(b) 50
(c) 45
(d) 35

Answer 1

Disclaimer: In the question ∠ACD should be 7y°.

In the given figure, ∠ACB + ∠ACD = 180° (Linear pair of angles)

∴ 5y° + 7y° = 180°

⇒ 12y° = 180°

⇒ y = 15 .....(1)

In ∆ABC,

∠A + ∠B + ∠ACB = 180° (Angle sum property)

∴ 3y° + x° + 5y° = 180°

⇒ x° + 8y° = 180°

⇒ x° + 8 × 15° = 180° [Using (1)]

⇒ x° + 120° = 180°

⇒ x° = 180° − 120° = 60°

Thus, the value of x is 60.

Hence, the correct answer is option (a).