Question

1. find the measure of the indicated angle

a. 78°
b. 54°
c. 111°
d. 107°

1. solve for x.

a. -6
b. 9
c. 7
d. -7

Explanation:

Step1: Identify the relationship between the angles (for question 1)

When two parallel lines are cut by a transversal, alternate - interior angles are equal. The given \(54^{\circ}\) angle and the angle \(y\) (the angle we want to find) are alternate - interior angles.

Step2: Solve for \(x\) (for question 2)

When two parallel lines are cut by a transversal, consecutive - interior angles are supplementary. So, \(- 2+16x + 110=180\).
First, simplify the left - hand side of the equation: \(16x+108 = 180\).
Then, subtract \(108\) from both sides: \(16x=180 - 108\), \(16x = 72\).
Finally, divide both sides by \(16\): \(x=\frac{72}{16}=9\).

Answer:

1. B. \(54^{\circ}\)
2. B. \(9\)