Question

1. find the value of x. name the angle pair used. 128° (2x + 8)° x = 60 corresponding 5. (9x - 2)° 47° find the measure of angle 1. name the angle pair(s) used. 6. 5x° (9x - 16)° 7. 6x° 1 (12x - 18)°

Explanation:

Step1: Identify angle - pair relationship for problem 6

The angles \(5x^{\circ}\) and \((9x - 16)^{\circ}\) are vertical angles. Vertical angles are equal.

$$5x=9x - 16$$

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides:

$$0 = 9x-5x - 16$$

$$0 = 4x - 16$$

Add 16 to both sides:

$$16 = 4x$$

Divide both sides by 4:

$$x = 4$$

Step3: Find the measure of angle 1

Angle 1 and \(5x^{\circ}\) are supplementary (linear - pair). The sum of angles in a linear - pair is \(180^{\circ}\).
First, find the measure of \(5x^{\circ}\) when \(x = 4\), so \(5x=5\times4 = 20^{\circ}\).
Then, the measure of angle 1 is \(180 - 20=160^{\circ}\). The angle - pairs used are vertical angles and linear - pair.

Step4: Identify angle - pair relationship for problem 7

The angles \(6x^{\circ}\) and \((12x - 18)^{\circ}\) are corresponding angles. Corresponding angles are equal when the lines are parallel.

$$6x=12x - 18$$

Step5: Solve the equation for \(x\)

Subtract \(6x\) from both sides:

$$0 = 12x-6x - 18$$

$$0 = 6x - 18$$

Add 18 to both sides:

$$18 = 6x$$

Divide both sides by 6:

$$x = 3$$

Step6: Find the measure of angle 1

Angle 1 and \(6x^{\circ}\) are supplementary (linear - pair).
First, find the measure of \(6x^{\circ}\) when \(x = 3\), so \(6x=6\times3 = 18^{\circ}\).
Then, the measure of angle 1 is \(180 - 18 = 162^{\circ}\). The angle - pairs used are corresponding angles and linear - pair.

Answer:

For problem 6: Measure of angle 1 is \(160^{\circ}\), Angle - pairs used: vertical angles and linear - pair.
For problem 7: Measure of angle 1 is \(162^{\circ}\), Angle - pairs used: corresponding angles and linear - pair.