Answer:
x = 9
m<J = 57
m<K = 44
m<L = 79
Explanation:
Theorem:
The sum of the measures of the angles of a triangle is 180°.
We add the measures of the angles, and set the sum equal to 180. Then we solve for x, and use the value of x to find the measure of each angle.
7x - 6 + 3x + 17 + 9x - 2 = 180
Combine like terms on the left side: 7x + 3x + 9x = 19x and -6 + 17 - 2 = 9
19x + 9 = 180
Subtract 9 from both sides.
19x = 171
Divide both sides by 19.
x = 9
Now we find the measure of each angle.
m<J = 7x - 6 = 7(9) - 6 = 63 - 6 = 57
m<K = 2x + 17 = 3(9) + 17 = 27 + 17 = 44
m<L = 9x - 2 = 9(9) - 2 = 81 - 2 = 79