Question

1. solve for x. x = __ m∠mat=__ 8. which angles are congruent to ∠2 and why are they congruent? a. ∠4 because they are vertical b. ∠1 because they are a linear pair c. ∠7 because they are corresponding d. ∠8 because they are alternate exterior

Explanation:

Step1: Set up the equation

Since vertical - angles are congruent, we set the two angle expressions equal to each other. Given \(8x + 15=5x + 21\).

Step2: Subtract \(5x\) from both sides

To get all the \(x\) - terms on one side, we have \((8x+15)-5x=(5x + 21)-5x\), which simplifies to \(3x+15 = 21\).

Step3: Subtract 15 from both sides

We want to isolate the \(x\) - term, so \((3x + 15)-15=21-15\), resulting in \(3x=6\).

Step4: Divide both sides by 3

To solve for \(x\), we do \(\frac{3x}{3}=\frac{6}{3}\), so \(x = 2\).

Answer:

\(x = 2\)