Question

Ray PK → bisects ∠LPM, the measure of ∠LPM is 11x°, and the measure of ∠LPK is (4x + 18)°. What is the measure of ∠KPM?

a) 12°
b) 28°
c) 42°
d) 66°

Answer 1

To calculate the measure of ∠KPM, we solved the equation (4x + 18)° + (4x + 18)° = 11x°. After finding x = 12, we determined that the measure of ∠LPK, as well as ∠KPM, is 66°. Therefore, the correct answer is D.

Step-by-step explanation:

To find the measure of ∠KPM, we must understand that ray PK bisects ∠LPM. Given that the measure of ∠LPM is 11x° and the measure of ∠LPK is (4x + 18)°, we can establish two facts:

• Since PK bisects ∠LPM, the two angles ∠LPK and ∠KPM are equal in measure.
• The sum of the measures of angles ∠LPK and ∠KPM is equal to the measure of ∠LPM.

Therefore, we can create the equation (4x + 18)° + (4x + 18)° = 11x° to represent the bisected angle. Solving for x, we have:

8x + 36 = 11x

36 = 3x

x = 12

Substitute x = 12 into the equation for ∠LPK to find its measure:

(4x + 18)° = (4(12) + 18)° = (48 + 18)° = 66°

Thus, the measure of ∠KPM is also 66°, meaning the correct answer is (d) 66°.