Question

1. if ∠5 = 5z - 20 and ∠8 = 3z + 10 are alternate exterior angles, solve for z.

a. 10
b. 15
c. 20
d. 25

Explanation:

Step1: Recall angle - property

Alternate exterior angles are equal. So, \(5z - 20=3z + 10\).

Step2: Isolate variable terms

Subtract \(3z\) from both sides: \(5z-3z - 20=3z-3z + 10\), which simplifies to \(2z-20 = 10\).

Step3: Isolate the variable

Add 20 to both sides: \(2z-20 + 20=10 + 20\), getting \(2z=30\).

Step4: Solve for \(z\)

Divide both sides by 2: \(\frac{2z}{2}=\frac{30}{2}\), so \(z = 15\).

Answer:

b. 15