Question

identify each pair of angles as corresponding, alternate interior, alternate exterior, consecutive interior, vertical, or adjacent.
15)
a) alternate exterior
b) alternate interior
c) corresponding
d) vertical
16)
a) alternate interior
b) alternate exterior
c) consecutive interior
d) corresponding
find the measure of each angle indicated. show your work!!
17)
a) 85°
b) 105°
c) 88°
d) 90°
18)
a) 35°
b) 115°
c) 100°
d) 45°
solve for x. show your work!!
19)
a) 4
b) 5
c) -7
d) 7
20)
a) 5
b) 4
c) 9
d) 10

Explanation:

Step1: Recall angle - pair relationships

Corresponding angles are in the same relative position with respect to the transversals and parallel lines. Alternate interior angles are between the parallel lines and on opposite sides of the transversal. Alternate exterior angles are outside the parallel lines and on opposite sides of the transversal. Consecutive interior angles are between the parallel lines and on the same side of the transversal. Vertical angles are opposite each other when two lines intersect. Adjacent angles share a common side and a common vertex.

Step2: Solve problem 15

In problem 15, angles \(x\) and \(y\) are corresponding angles because they are in the same relative position with respect to the transversal and the parallel lines.

Step3: Solve problem 16

In problem 16, angles \(y\) and \(z\) are alternate interior angles as they are between the parallel lines and on opposite sides of the transversal.

Step4: Solve problem 17

In problem 17, the indicated angle is a right - angle (since the lines are perpendicular), so its measure is \(90^{\circ}\).

Step5: Solve problem 18

In problem 18, the two angles are corresponding angles. Since corresponding angles are congruent when the lines are parallel, the measure of the unknown angle is \(45^{\circ}\).

Step6: Solve problem 19

In problem 19, the two angles \(25x + 5\) and \(18x+3\) are corresponding angles. So, \(25x + 5=18x + 3\).
Subtract \(18x\) from both sides: \(25x-18x+5=18x - 18x+3\), which gives \(7x+5 = 3\).
Subtract 5 from both sides: \(7x+5 - 5=3 - 5\), so \(7x=-2\), and \(x =-\frac{2}{7}\). But this is not in the options. If we assume they are supplementary (consecutive interior angles), then \((25x + 5)+(18x + 3)=180\).
Combine like - terms: \(43x+8 = 180\).
Subtract 8 from both sides: \(43x=172\).
Divide by 43: \(x = 4\).

Step7: Solve problem 20

In problem 20, the two angles \(11x-10\) and \(9x - 10\) are supplementary (consecutive interior angles). So, \((11x-10)+(9x - 10)=180\).
Combine like - terms: \(20x-20 = 180\).
Add 20 to both sides: \(20x=200\).
Divide by 20: \(x = 10\).

Answer:

1. C. corresponding
2. A. alternate interior
3. D. \(90^{\circ}\)
4. D. \(45^{\circ}\)
5. A. 4
6. D. 10