An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles is
a) 37 1/2 °
b) 52 1/2 °
c) 72 1/2 °
d) 75°

Solution:

Given, the exterior angle of a triangle is 105°

Also, two interior opposite angles are equal.

We have to find the measure of each of these equal angles.

We know that an exterior angle of a triangle is equal to the sum of the corresponding two interior opposite angles.

Let the interior angle be x

Now, x + x = 105°

2x = 105°

x = 105°/2

x = 52 1/2°

Therefore, the measure of each equal angles is 52 1/2°

✦ Try This: An exterior angle of a triangle is 125° and its two interior opposite angles are equal. Each of these equal angles is

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6

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NCERT Exemplar Class 9 Maths Exercise 6.1 Problem 3

An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles is a) 37 1/2 °, b) 52 1/2 °, c) 72 1/2 °, d) 75°

Summary:

An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles is 52 1/2°

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