The m<GKJ = 56o, m<GKH = 4x + 2, and m<JKH = 7x - 12. Solve for the measures of angles GKH and JKH. (2 points) m<GKH = degrees m<JKH = degrees
To solve for the measures of angles GKH and JKH, we can use the fact that the sum of the measures of the angles in a triangle is always 180 degrees.
So, we have:
m<GKJ + m<GKH + m<JKH = 180
Substituting the given values, we get:
56 + (4x + 2) + (7x - 12) = 180
Simplifying the equation, we get:
11x + 46 = 180
Subtracting 46 from both sides, we get:
11x = 134
Dividing both sides by 11, we get:
x = 134/11
Therefore, x ≈ 12.18.
To find the measure of angle GKH, we substitute x back into the equation:
m<GKH = 4x + 2 = 4(12.18) + 2
m<GKH ≈ 48.72 + 2 ≈ 50.72 degrees
To find the measure of angle JKH, we also substitute x back into the equation:
m<JKH = 7x - 12 = 7(12.18) - 12
m<JKH ≈ 85.26 - 12 ≈ 73.26 degrees
Therefore, the measure of angle GKH is approximately 50.72 degrees and the measure of angle JKH is approximately 73.26 degrees.