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
Solution:
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).