The sum of the measures of the angles of a triangle is 180 degrees.

Question

The smallest angle of the triangle has a measure 4/5 the measure of the second smallest angle. The largest angle has a measure that is 23 degrees less than 4 times the measure of the second smallest angle. Determine the measure of each angle.

Answer 1

The strategy for solving this problem is to first find the measure of one angle, then to use that to find the measure of the other angles.

Two angles are described in terms of the second smallest angle; use that information.

Angle A: (smallest angle) A = (4/5)B

Angle B: (second smallest angle) = B

Angle C: (largest angle)) C = 4B- 23

The sum of the three angles of a triangle = 180.

A + B + C = 180

(4/5)B + B + (4B-23) = 180

4B + 5B + 20B - 115 = 900 [multiply by LCD=5]

29B = 1015

B = 35

A = (4/5)(35) = 28

C = 4(35)-23 = 117

Check:

Does 28 + 35 + 117 = 180 ?

180 = 180 ?yes