Question

An exterior angle of a triangle has a measure of 130 degree. The remote

interior angles in the ratio of 2:3. Find the measure of the largest angle of
the triangle.

Answer 1

• 78°

Explanation:

The exterior angle measure is same as he sum of remote interior angles and the adjacent interior angle make straight angle with the exterior angle

So the adjacent angle is:

• 180 - 130 = 50°

The other angles are 2x and 3x as per ratio:

• 2x + 3x = 130
• 5x = 130
• x = 130/5
• x = 26

And

• 2x =2*26 = 52°
• 3x = 2*26 = 78°

So the angles are:

• 50°, 52°, 78°

The largest angle is 78°