In a triangle, the measure of the first angle is three times the measure of the second angle. The measure of the third angle is 55 more than the measure of the second angle. Use the fact that the sum of the measures of the three angles is 180 to find the measure of each angle to find the measure of each angle.

QUESTION POSTED AT 02/06/2020 - 01:21 AM

Answered by admin AT 02/06/2020 - 01:21 AM

Let the angles be A, B, C where B is the second angle.

"measure of the first angle is three times the measure of the second angle" =>
A=3B
 
"The measure of the third angle is 55 more than the measure of the second angle" =>
C=B+55
 
We know that A+B+C=180, =>
A+B+C=180=(3B+B+B+55)
=>
5B=180-55=125
B=25 degrees
A=3*25=75
C=25+55=80
Check: A+B+C=75+25+80=180 ok!


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