Answer:
∠ GKH = 39° , ∠ MNQ = 25°
Explanation:
12
from the diagram
∠ GKJ and ∠ GKH form ∠ JKH , that is
∠ GKJ + ∠ GKH = ∠ JKH = 90°
substitute the given angles, equate to 90 and solve for x
13x - 1 + 9x + 3 = 90 ( simplify left side )
22x + 2 = 90 ( subtract 2 from both sides )
22x = 88 ( divide both sides by 22 )
x = 4
Then
∠ GKH = 9x + 3 = 9(4) + 3 = 36 + 3 = 39°
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13
∠ MNQ and ∠ RNP are vertically opposite angles and are congruent , then
∠ RNP = ∠ MNQ
5x - 40 = 2x - 1 ( subtract 2x from both sides )
3x - 40 = - 1 ( add 40 to both sides )
3x = 39 ( divide both sides by 3 )
x = 13
Then
∠ MNQ = 2x - 1 = 2(13) - 1 = 26 - 1 = 25°