7. in triangle abc, the measure of angle a is twenty-five degrees more than the measure of angle c, and the measure of angle b is 40o more than the measure of angle c. what are the measures of the angles of the triangle?

angle A = 63.3 degrees

angle B = 78.3 degrees

angle C = 38.3 degrees

Step-by-step explanation:

In triangle ABC, the measure of angle A is twenty-five degrees more than the measure of angle C. This means that

angle A = angle C + 25 degrees

The measure of angle B is 40 degrees more than the measure of angle C. This means that

angle B = angle C + 40

The equations are

A = C + 25 - - - - - - - -1

B = C + 40 - - - - - - - - - 2

Recall, the sum of angles in a triangle is 180 degrees. Therefore,

A + B + C = 180 - - - - - - 3

Substituting equation 1 and equation 2 into equation 3, it becomes

C + 25 + C + 40 + C = 180

3C + 65 = 180

3C = 180 - 65 = 115

C = 115/3 = 38.3 degrees

Substituting C = 38.3 into equation 1 and equation 2, it becomes

A = 38.3 + 25 = 63.3 degrees

B = 38.3 + 40 = 78.3 degrees

Sum of angle A, angle B and angle C = 63.3 + 78.3 +38.3 = 79.9 degrees.

Approximately 180 degrees

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