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Question

The sum of the measures of the angles of a triangle is 180 degrees. The middle-sized angle measures 5 degrees more than 4 times the smallest angle. The middle-sized angle measures 53 degrees less that the largest angle.
Find the measures of each angle.

Answer 1

Let x = the smallest angle.  The middle angle is 5 degrees more than 4 times the smallest angle, or 4x+5.  The largest angle is 53 degrees more than the middle angle, or (4x+5)+53 = 4x + 58  All three angles must add up to 180°

 

x + 4x+5 + 4x+58 = 180°

9x + 63 = 180

9x = 117

x = 13°

 

The smallest angle = 13°

The middle angle = 4x+5 = 4(13)+5 = 57°

The largest angle = 57+53 = 110°