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1 Answer

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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°

User Shawn Grigson
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