Question

$\text{In the given figure, side BC of}\Delta ABC\text{has been produced to a point D.If}\angle A=3y^{\circ },\angle x^{\circ },\angle C5y^{\circ }and\angle CBD=7y^{\circ }.Then.thevalueofxis$

$\left(a\right){60}^{\circ }\left(b\right){50}^{\circ }\left(c\right){45}^{\circ }\left(d\right){35}^{\circ }$

Answer 1

NSWER:
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° + 5 y° = 180°
⇒ x° + 8 y° = 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).