Question

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Ray PK bisects ∠LPM, the measure of ∠LPM is 11x°,
5θ⎪−_π_<θ<_π_6 _π_ _π_
and the measure of ∠LPK is (4x + 18)°. What is the measure of ∠KPM ?

Answer 1

The measure of ∠KPM is 66°

Explanation:

we know that

∠LPM=∠LPK+∠KPM

If ray PK bisects ∠LPM

then

∠LPK=∠KPM

and

∠LPM=2[∠LPK] -----> equation A

we have

∠LPM=11x°

∠LPK=(4x+18)°

substitute the values in equation A

11x°=2(4x+18)°

Solve for x

11x=8x+36

11x-8x=36

3x=36

x=12°

Find the measure of angle ∠LPK

∠LPK=(4x+18)°

substitute the value of x

∠LPK=(4(12)+18)=66°

Remember that

∠LPK=∠KPM

therefore

∠KPM=66°