Answer: ∠LKM=56° and ∠MKN=89°
Explanation:
Notice that ∠LKM and ∠MKN make up ∠LKN. That means ∠LKM and ∠MKN combines equals 145°.
2x+10+4x-3=145 [combing like terms]
6x+7=145 [subtract both sides by 7]
6x=138 [divide both sides by 6]
x=23
We are almost done. We still need to plug it in to find the angle values.
∠LKM
2x+10 [plug in x=23]
2(23)+10 [multiply]
46+10 [add]
56
∠LKM=56°
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∠MKN
4x-3 [plug in x=23]
4(23)-3 [multiply]
92-3 [subtract]
89
∠MKN=89°
Therefore, ∠LKM=56° and ∠MKN=89°.