Question

Two angles of triangle are equal and third angle is greater than each of these angles by 45°. Find the degree of greatest angle. 
1. 90° 
2. 45° 
3. 22.5° 
4. 27° 

Answer 1

Correct Answer - Option 1 : 90° 

Given:

Two angles are equal.

The third angle is 45°more than the base angle

Calculation:  

Let assume that equal angles measure is x

And, third angle = x + 45° 

According to the question

⇒ x + x + x + 45° = 180° 

⇒ 3x + 45° = 180° 

⇒ 3x = 180° - 45° 

⇒ 3x = 135° 

⇒ x = 135°/3

⇒ x = 45°

Greatest angle = x + 45° 

⇒ 45° + 45° = 90° 

∴ The greatest angle is 90°