Question

m∠cdl = 38°, m∠cde = 13x + 15, and m∠lde = 11x - 1. find x.

Explanation:

Step1: Use angle - addition postulate

Since $\angle CDE=\angle CDL+\angle LDE$, we can write the equation $13x + 15=38+(11x - 1)$.

Step2: Simplify the right - hand side

Simplify $38+(11x - 1)$ to get $11x+37$. So the equation becomes $13x + 15=11x + 37$.

Step3: Subtract $11x$ from both sides

$13x-11x + 15=11x-11x + 37$, which simplifies to $2x+15 = 37$.

Step4: Subtract 15 from both sides

$2x+15 - 15=37 - 15$, resulting in $2x=22$.

Step5: Divide both sides by 2

$\frac{2x}{2}=\frac{22}{2}$, so $x = 11$.

Answer:

$x = 11$