SOLUTION: in triangle abc, measure of angle a= 2x+3, measure b= 3x+5, and measure c= 5x+2. Solve for x and find the measure of eace angle.

Question 78929: in triangle abc, measure of angle a= 2x+3, measure b= 3x+5, and measure c= 5x+2. Solve for x and find the measure of eace angle.
Found 2 solutions by tutor_paul, sprolden:
Answer by tutor_paul(519) (Show Source): You can put this solution on YOUR website!
The key to this problem is to recognize that the sum of the angles of a triangle always add up to 180. So you can set up an equation like this:

combine the like terms:

solve for x:

To find the measure of each angle, just plug x back into the equation of each angle. i will do one, you can do the other two:

substitute in your value of x:

Good Luck,
tutor_paul@yahoo.com
Answer by sprolden(40) (Show Source): You can put this solution on YOUR website!
ANGLES a= 2x+3 b= 3x+5 c= 5x+2
1- ADD THE MEASURES OF ALL ANGLES TOGETHER AND SET THEM EQUAL TO 180 DEGREES. THERE ARE 180 DEGREES IN A TRIANGLE. 2x+3 + 3x+5 + 5x+2 = 180
2- COMBINE LIKE TERMS 2x + 3x + 5x = 10x and 3 + 5 + 2 = 10
3- COMBINE THE SUMS OF THE TERMS 10x+10 = 180
4- SOLVE FOR X BY FIRST SUBTRACTING 10 FROM EACH SIDE 10x+10-10 = 180-10
5- YOU SHOULD GET 10x = 170
6- DIVIDE BOTH SIDES BY 10--- 10X/10 = 170/10, SO x=17
7- SUBSTITUTE THE VALUE OF x BACK INTO EACH EXPRESSION
a= 2x+3 2(17)+3= 37 degrees
b= 3x+5 3(17)+5= 56 degrees
c= 5x+2 5(17)+2= 87 degrees
8- NOTICE THAT THE SUM OF 87+56+37=180, SINCE THERE ARE 180 DEGREES IN A TRIANGLE.
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