Answer:
- angle PKL = 113 degrees
- angle NKO = 23 degrees
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Step-by-step explanation:
Refer to the diagram below.
Angle JKP is marked in red, and it's 67 degrees.
Angle PKL is marked in green, and it's right next to angle JKP. The two angles combine to form a straight line. This means the angle measures add to 180.
So,
(angleJKP) + (anglePKL) = 180
anglePKL = 180 - (angleJKP)
anglePKL = 180 - (67)
anglePKL = 113
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Angle MKL is a right angle, aka 90 degree angle. This is indicated by the square marker in the diagram.
Subtract this from the angle PKL we just found. This will get us the measure of angle PKM
anglePKM = anglePKL - angleMKL
anglePKM = 113 - 90
anglePKM = 23
This is congruent to angle NKO because angles PKM and NKO are vertical angles. Vertical angles are always congruent.
Therefore, angleNKO = 23.
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Another approach you could take is to see that angles JKP and LKO are vertical angles. So angleLKO = 67.
Then notice how,
angleLKO+angleNKO = 90
angleNKO = 90-angleKLO
angleNKO = 90-67
angleNKO = 23