Find the measure of the third angle

Question

The measure of one angle of a triangle is 1 less than twice the measure of the second angle, and the measure of the third angle is 21 more than twice the sum of the measures of the other two. Find the measure of the third angle.

Answer 1

Hi Nicole

let's break you problem in small parts. Let call your angles A, B and C

1. The measure of one angle (let's say A) of a triangle is 1 less than twice the measure of the second angle(let's say B), this means: m(A)=2•m(B)-1
2. and the measure of the third angle (C) is 21 more than twice the sum of the measures of the other two: this means that m(C)=21+2•(m(A)+m(B)). but we already know that m(A)=2•m(B)-1 therefore our third angle can we written as m(C)=21+2•(2•m(B)-1+m(B)). if we further simplify we get: m(C)=21+2•(3m(B)-1) or m(C)=6m(B)+19

Now we need a triangle property which says that "The sum of measure of all angles in a triangle is 180"

m(A)+m(B)+m(C)=180

but we know that m(A)=2•m(B)-1 and m(C)=6m(B)+19

Inserting these two above we get:

2•m(B)-1 + m(B)+6m(B)+19=180

Solving for measure of B we get:

2m(B)+m(B)+6m(B)=180+1-19

9m(B)=162

m(B)=18

Now m(C) (your third angle)can be easily found:

m(C)=6m(B)+19=6•18+19=127