Question

"In ABC, mBAC = 5x + 8, mABC = 6x + 22, and mBCA = 3x  25.

A.Find the value of x.
B.Find the measure of 3. Show your work."

Answer 1

Actually, the answer is 12.5

5x+8+6x+22+3x+25= 180

(5x+6x+3x)+(8+22-25)= 180

14x+5=180

14x+(5-5)=180-5

14x=175

14x/14=175/14

X=12.5

Double check:

(5*12.5)+8=70.5

(6*12.5)+22= 97

(3*12.5)-25=12.5

70.5+97+12.5=180 degrees.

So, x=12.5

Answer 2

In angle ABC, the measure of angle BAC = 5x + 8, measure of angle ABC = 6x + 22, and measure of angle BCA = 3x  25. You know that the sum of the angles of a triangle is 180 degrees. And since the angles BAC, ABC and BCA are the corners of the triangle then just add them and equate to 180 degrees.

5x + 8 + 6x + 22 + 3x + 25 = 180
14x + 55 = 180
14x = 125
x = 8.93