The m<GKJ = 56o, m<GKH = 4x + 2, and m<JKH = 7x - 12. Solve for the measures of angles GKH and JKH.
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To solve for the measures of angles GKH and JKH, we need to set up an equation based on the given information.
We know that the sum of the measures of angles in a triangle is 180 degrees. Therefore, we can write the equation:
m<GKJ + m<GKH + m<JKH = 180
Substituting the given values, we get:
56 + (4x + 2) + (7x - 12) = 180
Combine like terms:
56 + 4x + 2 + 7x - 12 = 180
11x + 46 = 180
Subtract 46 from both sides:
11x = 180 - 46
11x = 134
Divide both sides by 11:
x = 134 / 11
x ≈ 12.18
Now, substitute this value of x to find the measures of angles GKH and JKH:
m<GKH = 4x + 2 = 4(12.18) + 2 ≈ 49.72
m<JKH = 7x - 12 = 7(12.18) - 12 ≈ 75.26
Therefore, m<GKH ≈ 49.72 degrees and m<JKH ≈ 75.26 degrees.