in the figure, ∠rqs ≅ ∠qlk. what is the value of x? 36 72 108 144

Explanation:

Step1: Use angle - congruence property

Since $\angle RQS\cong\angle QLK$, we can set up an equation based on the angle measures. The measure of $\angle RQS = x^{\circ}$ and the measure of $\angle QLK=(x - 36)^{\circ}$. $x=x - 36$ is incorrect. We know that $\angle RQS$ and $\angle QLK$ are corresponding angles. Corresponding angles formed by parallel lines (assuming the lines are parallel, which is a common situation in such angle - congruence problems) are equal. So we set up the equation $x+(x - 36)=180$ (because they are supplementary angles).

Step2: Solve the equation

First, expand the left - hand side of the equation: $x+x - 36=180$. Combine like terms: $2x-36 = 180$. Add 36 to both sides of the equation: $2x=180 + 36$. $2x=216$. Divide both sides by 2: $x=\frac{216}{2}=108$.

Answer:

108