Question

in the picture, line a is parallel to line b. m∠4 = 9x - 5 and m∠5 = 4x + 16. what kind of angle pair is ∠4 & ∠5? what is the equation you can use to solve for x? equation: 9x - 5 = 4x + 16

Explanation:

Step1: Set up the equation

Since $\angle4$ and $\angle5$ are alternate - interior angles (AIA) and line $a$ is parallel to line $b$, alternate - interior angles are congruent. So we set up the equation $9x - 5=4x + 16$.

Step2: Isolate the variable terms

Subtract $4x$ from both sides of the equation:
$9x-4x - 5=4x-4x + 16$
$5x-5 = 16$

Step3: Isolate the variable

Add 5 to both sides:
$5x-5 + 5=16 + 5$
$5x=21$

Step4: Solve for x

Divide both sides by 5:
$x=\frac{21}{5}=4.2$

Answer:

$x = 4.2$