General Aptitude TestQuantitative ReasoningGeometry

In the given figure, if AC, DE are parallel and ∠CAB = 38° , then the…

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

Answer & explanation

Correct answer: option 3

We have,

∠CAB = 38

∠ABC = b

∠CBD = a

∠CAB = 2a

According to the question,

2a = 38^o

∠CBD = a = 19^o

∠CAB + ∠ABD = 180 (Because AC and BD are parallel)

⇒ 2a + b + a = 180^o

⇒ 38 + b + 19 = 180^o

⇒ b = 180 - 57

⇒ b = 123^o

∴∠ABC = 123^o

Now, ∠ABC + 5 ∠CBD

= 123 + 5 × 19

= 123 + 95 = 218^o