find the measure of the angles of a triangle. the second angle is five times the first. the third angle is 81 degrees more than the second

Question

find the measure of the angles of a triangle. the second angle is five times the first. the third angle is 81 degrees more than the second

Answer 1

Here's what we know:

a + b + c = 180 (triangle angles add up to 180)

b = 5a (the second angle is five times the first)

c = b + 81 (the third is 81 more than the second)

 

Plug in the variables:

a + 5a + b + 81 = 180

a + 5a + 5a + 81 = 180

simplify:

11a + 81 = 180

Subtract 81:

11a = 99

Divide by 11:

a = 9

 

b = 5 * 9

b = 45

 

c = 45 + 81

c = 126

 

Check:

9 + 45 + 126 = 180

180 = 180

Answer 2

f + 5f + 5f + 81 = 180

11f = 99

f = 9

 

9, 45, 126