Question

A right triangle has exterior angles at each of its acute angles with measures in te ratio 13:14. find the measures o the two acute angles of the right triangle.

Answer 1

The sum of the exterior angles of all polygon is always equal to 360°. The exterior angle sharing the same side with that of the right angle of the triangle is equal to 90°. If the other exterior angles are 13x and 14x then, they add up to 270°. 

The equation that would allow us to determine the values of the angles are,
                          13x + 14x = 270
                              x = 10
The exterior angles are 130 and 140°. The exterior angle and the interior angle always add up to 180°. 

Interior angle 1:   180° - 130° = 50°
Interior angle 2:    180° - 140° = 40°

Therefore, the measures of the two acute angles of the triangle are 50° and 40°.