Question

In the given figure, side BC of ΔABC has been produced to a point D. If ∠A = 3y0, ∠B = x0, ∠ACB = 5y0 and ∠CBD = 7y0, then the value of x is:
(a) 60

(b) 50

(c) 45

(d) 30​

Answer 1

Given: If ∠A = 3y°, ∠B = x°, ∠ACB = 5y° and ∠CBD = 7y°

To find: The value of x

Solution:

In the question ∠ACD should be 7y°.

In the given figure, ∠ACB + ∠ACD = 180°

(Linear pair of angles)

Therefore,

5y° + 7y° = 180°

⇒ 12y° = 180°

⇒ y = 15 ....(1)  

In ∆ABC,

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

Therefore,

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).

Answer 2

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

In ∆ABC,

∠A + ∠B + ∠ACB = 180°

(Angle sum property)

∴ 3y° + x° + 5 y° = 180°

⇒ x° + 8 y° = 180°

⇒ x° + 8 × 15° = 180°

⇒ x° + 120° = 180°

⇒ x° = 180° − 120° = 60°

Thus, the value of x is 60.

Hence, the correct answer is option (a).

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