SOLUTION: The first angle of a triangle is twice the measure of the second angle. The third angle is 10 degree less than the measure of the first angle. Find the measure of each angle.

Algebra ->  Rectangles -> SOLUTION: The first angle of a triangle is twice the measure of the second angle. The third angle is 10 degree less than the measure of the first angle. Find the measure of each angle.      Log On


   



Question 351931: The first angle of a triangle is twice the measure of the second angle. The third angle is 10 degree less than the measure of the first angle. Find the measure of each angle.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For any triangle,
a%5B1%5D%2Ba%5B2%5D%2Ba%5B3%5D=180
.
.
a%5B1%5D=2%2Aa%5B2%5D
a%5B2%5D=%281%2F2%29a%5B1%5D
.
.
a%5B3%5D=a%5B1%5D-10
Substitute,
a%5B1%5D%2B%281%2F2%29a%5B1%5D%2Ba%5B1%5D-10=180
%285%2F2%29a%5B1%5D-10=180
%285%2F2%29a%5B1%5D=190
highlight%28+a%5B1%5D=76%29degrees
Then
a%5B2%5D=%281%2F2%2976
highlight%28a%5B2%5D=38%29degrees
and,
a%5B3%5D=76-10
highlight%28a%5B3%5D=66%29degrees