Question

what is the measure of ∠4 if ∠4 = 4a + 30 and a = 15?
a. 85 degrees
b. 90 degrees
c. 95 degrees
d. 80 degrees

if ∠5 = 5z - 20 and ∠8 = 3z + 10 are alternate exterior angles, solve for z.
a. 25
b. 15
c. 10
d. 20

Explanation:

Step1: Substitute value of a

Given $\angle4 = 4a+30$ and $a = 15$. Substitute $a$ into the formula: $\angle4=4\times15 + 30$.

Step2: Calculate the value of $\angle4$

$4\times15+30=60 + 30=90$. So the measure of $\angle4$ is 90 degrees.

Step3: Use property of alternate - exterior angles

Since $\angle5$ and $\angle8$ are alternate - exterior angles, $\angle5=\angle8$. So $5z-20 = 3z+10$.

Step4: Solve the equation for z

First, subtract $3z$ from both sides: $5z-3z-20=3z - 3z+10$, which simplifies to $2z-20 = 10$. Then add 20 to both sides: $2z-20 + 20=10 + 20$, getting $2z=30$. Divide both sides by 2: $z = 15$.

Answer:

1. b. 90 degrees
2. b. 15