One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 10 degrees larger smallest angle.

Question

the largest angle has a measure of how many degrees?

Answer 1

a) Define the problem:

A triangle by definition is tri + angle = 3 angles.

All 3 angles must sum to 180 degrees.

a = smallest angle

b = second angle

c = third angle

 

b) Set up the relationships:

equation 1: a + b + c = 180

equation 2: b = 3a

equation 3: c = a + 10

 

c) Solve the problem:

Substitute eq. 2 and eq. 3 into eq. 1.

a + 3a + (a+10) = 180

5a + 10 = 180

a = 34

Substitute a into eq. 2

b = 3 * 34 = 102

Substitute a into eq. 3

c = 34 + 10 = 44

Answer: The largest angle of 34, 44, and 102 is 102 degrees.