Question

One of the exterior angle of a triangle is 105° and the interior opposite angles are in the ratio 2 : 5. Find the angles of the triangle.

Answer 1

Ratio of interior opposite angles = 2 : 5 

Sum of the terms of the ratio = 2 + 5 = 7 

Sum of the angles = 105° 

∴ 1st angle = 2/7 x 105° = 30° 

2nd angle = 5/7 x 105° = 75° 

3rd angle = 180° – (30° + 75°) 

[∵ angle – sum property] 

= 180° – (105°) = 75°