Question

the measure of angle jkl can be represented using the expression 3x + 5. what is the degree measure of ∠jkl?

Explanation:

Step1: Analyze angle composition

From the diagram, $\angle JKL = \angle JKM + \angle MKL$. We know $\angle JKM = 45^\circ$, $\angle MKL = x^\circ$, and $\angle JKL = 3x + 5$. So the equation is $3x + 5 = 45 + x$.

Step2: Solve for x

Subtract $x$ from both sides: $3x - x + 5 = 45 + x - x$ → $2x + 5 = 45$.
Subtract 5 from both sides: $2x + 5 - 5 = 45 - 5$ → $2x = 40$.
Divide by 2: $x = \frac{40}{2} = 20$.

Step3: Find $\angle JKL$

Substitute $x = 20$ into $3x + 5$: $3(20) + 5 = 60 + 5 = 65$.

Answer:

65