In the description

Question

In triangle ABC, the measure of angle B is 31 degrees more than three times the measure angle of angle A. The measure of angle C is 59 degrees more than the measure of angle A. Find the measure of each angle.

Answer 1

Here's what we know:

a + b + c = 180 (all triangles are composed of 180 degrees)

b = 3a + 31 (b is 31 more than a times three)

c = a + 59 (c is 59 degrees more than a)

 

Now that we have values for our variables, let's plug them in:

a + (3a + 31) + (a + 59) = 180

combine like terms:

5a + 90 = 180

Subtract 90:

5a = 90

Divide by 5:

a = 18

 

Now to find the other variables:

b = 3 * 18 + 31

b = 54 + 31

b = 85

 

c = 18 + 59

c = 77

 

Check:

18 + 85 + 77 = 180

95 + 85 = 180

180 = 180