Question

1. find the measure of the indicated angle:

a. 115°
b. 98°
c. 180°
d. 76°

1. solve for x.

a. 9
b. 7
c. -8
d. 11

Explanation:

Question 1

Step1: Use the property of alternate interior angles

When two parallel lines are cut by a transversal, alternate interior angles are equal.

Step2: Identify the angle relationship

The given \(98^{\circ}\) angle and the indicated angle are alternate interior angles.

Step1: Set up the equation

Since the two angles (\(15x + 5\) and \(16x-2\)) are equal (alternate interior angles for parallel lines cut by a transversal), we have the equation \(15x + 5=16x-2\).

Step2: Solve the equation for \(x\)

Subtract \(15x\) from both sides: \(5=x - 2\).
Then add \(2\) to both sides: \(x=5 + 2=7\).

Answer:

B. \(98^{\circ}\)

Question 2