Question

for 30 and 31 answer either a w or congruent.
30 ∠4 and ∠6
31 ∠1 and ∠8

for 32-33 find the slope that given points.
32 a(5,8) b(7,11)
33 c(0,7) d(4,8)

Explanation:

Step1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Calculate slope for problem 32

For points \( A(5, 8) \) and \( B(7, 11) \), let \( x_1 = 5 \), \( y_1 = 8 \), \( x_2 = 7 \), \( y_2 = 11 \).
Substitute into the formula: \( m=\frac{11 - 8}{7 - 5}=\frac{3}{2} \).

Step3: Calculate slope for problem 33

For points \( C(0, 7) \) and \( D(4, 8) \), let \( x_1 = 0 \), \( y_1 = 7 \), \( x_2 = 4 \), \( y_2 = 8 \).
Substitute into the formula: \( m=\frac{8 - 7}{4 - 0}=\frac{1}{4} \).

Answer:

• Problem 32: The slope is \(\frac{3}{2}\)
• Problem 33: The slope is \(\frac{1}{4}\)