In the given figure, if AC, DE are parallel and ∠CAB = 38ᵒ, then the value of ∠ABC + 5∠CBD is: [Image]

In the given figure, if AC, DE are parallel and ∠CAB =…

In the given figure, if AC, DE are parallel and ∠CAB = 38^o, then the value of ∠ABC + 5∠CBD is:

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e 218^o

Understanding

Application

We will gonna use properties of parallel lines, we know that alternate angles will be equal.

Given that,

∠CAB = 38^o= 2a

⇒ a = 19^o

By alternate angle theorem

∠ACB = ∠CBD

In triangle ABC, sum of angles would be,

⇒ 38^o + 19^o + ∠b = 180^o

⇒ ∠b = 123^o

∠ABC + 5∠CBD = b + 5a

⇒ 123^o + 5(19^o)

⇒ 123^o + 95^o

⇒ 218^o