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

Given that Ray PK bisects ∠LPM, this means that ∠LPK and ∠KPM are equal in measure.

We are given that the measure of ∠LPM is 11x° and the measure of ∠LPK is (4x + 18)°.

Since ∠LPK = ∠KPM, we can also say that the measure of ∠KPM is (4x + 18)°.

Now, since ∠LPM is the sum of ∠LPK and ∠KPM, we can set up the following equation:

11x = (4x + 18) + (4x + 18)

Solving this equation will give us the value of x, which we can then substitute back into the expression for the measure of ∠KPM to find its measure.

Let's solve the equation:

11x = 8x + 36

Subtract 8x from both sides:

3x = 36

Divide both sides by 3:

x = 12

Now, substitute x = 12 into the expression for the measure of ∠KPM:

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

So, the measure of ∠KPM is 66°.