Question

3.
a
b
96°
(6x - 30)°
6x-30=96
converse: ____
5.
(8x - 17)°
(5x + 19)°
a
b
converse: ____
7.
(6x + 5)°
(8x - 37)°
a
b
converse: ____

Explanation:

Problem 3

Step1: Identify the relationship

Since lines \(a\) and \(b\) are parallel (vertical lines with same direction), the given angles are equal (corresponding angles). So we set \(6x - 30=96\).

Step2: Solve for \(x\)

Add 30 to both sides: \(6x=96 + 30=126\).
Divide by 6: \(x=\frac{126}{6}=21\).

Step1: Identify the relationship

Lines \(a\) and \(b\) are parallel, so the alternate - interior angles are equal. Thus, \(8x-17 = 5x + 19\).

Step2: Solve for \(x\)

Subtract \(5x\) from both sides: \(8x-5x-17=5x - 5x+19\), \(3x-17 = 19\).
Add 17 to both sides: \(3x=19 + 17=36\).
Divide by 3: \(x=\frac{36}{3}=12\).

Step1: Identify the relationship

Lines \(a\) and \(b\) are parallel, so the alternate - interior angles are equal. Thus, \(6x + 5=8x-37\).

Step2: Solve for \(x\)

Subtract \(6x\) from both sides: \(6x-6x + 5=8x-6x-37\), \(5 = 2x-37\).
Add 37 to both sides: \(5 + 37=2x-37 + 37\), \(42=2x\).
Divide by 2: \(x=\frac{42}{2}=21\).

Answer:

\(x = 21\)

Problem 5