Final answer:
By setting the equations for the bisected angles equal to each other and solving for x, we find x = 11. Plugging x back into the equation for either angle gives us the measure of ∠KLN as 96°.
Step-by-step explanation:
If ray LM bisects ∠KLN, then angles KLM and MLN are equal. Given m∠KLM = 4x + 4 and m∠MLN = 2(x + 13), we can set up an equation since the measures of these two angles are equal because of the bisection.
4x + 4 = 2(x + 13)
Now, we need to solve for x:
- Expand the right side: 4x + 4 = 2x + 26
- Subtract 2x from both sides: 2x + 4 = 26
- Subtract 4 from both sides: 2x = 22
- Divide both sides by 2: x = 11
Now that we have the value for x, we can find the measure of KLN by plugging it back into the expression for either angle (since they are equal).
m∠KLN = 2∠KLM = 2(4x + 4)
Plug x = 11 into the equation: m∠KLN = 2(4(11) + 4) = 2(44 + 4) = 2(48) = 96°
Therefore, the measure of ∠KLN is 96°.
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