Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.