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RRB NTPC Mains or Stage 2 Model Paper 3 with solutions

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Question : 9 of 120

Marks: +1, -0

The side BC of △ ABC is produced to D. I f ,

\angle B = \frac{1}{2} \angle A

36°
72°
108°
59°

Solution:

Concept:

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Explanation:

Let

\angle A = x

.

Given

\angle B = \frac{1}{2}\angle A = \frac{x}{2}

.

The exterior angle

\angle ACD

equals

\angle A + \angle B

.

So,

108^\circ = x + \frac{x}{2}

.

This gives

108^\circ = \frac{3x}{2}

.

Therefore,

x = \frac{108^\circ \times 2}{3}

.

So,

x = 72^\circ

.

Hence,

\angle A = 72^\circ

.

Answer:

Option B:

72^\circ

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