Question

use the following diagram for 1 - 9. a||b, g||h (4 pts each)

1. the special angle - pair name for ∠1 and ∠14 is (g6a)

a. corresponding b. alternate interior c. alternate exterior d. consecutive/same - side interior

1. the special angle - pair name for ∠8 and ∠10 is (g6a)

a. corresponding b. alternate interior c. alternate exterior d. consecutive/same - side interior

1. the special angle - pair name for ∠4 and ∠6 is (g6a)

a. corresponding b. alternate interior c. alternate exterior d. consecutive/same - side interior

1. the special angle - pair name for ∠11 and ∠13 is (g6a)

a. corresponding b. alternate interior c. alternate exterior d. consecutive/same - side interior

1. ∠3 and ∠5 are (g6a)

a. congruent b. complementary c. supplementary d. bisected

1. ∠6 and ∠8 are (g6a)

a. vertical angles b. complementary angles c. linear pair d. corresponding angles

1. if m∠15 = 64°, then the measure of m∠10 is (g6a)

a. 26° b. 64° c. 32° d. 116°

1. if m∠16 = 106°, then the measure of m∠10 is (g6a)

a. 106° b. 74° c. 53° d. 16°

1. which is a pair of vertical angles? (g6a)

a. ∠1 and ∠2 b. ∠1 and ∠5 c. ∠3 and ∠5 d. ∠2 and ∠3

Explanation:

Step1: Recall angle - pair definitions

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/same - side 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.

Step2: Analyze each question

Question 1

$\angle1$ and $\angle14$ are alternate exterior angles since they are outside the parallel lines $a\parallel b$ and $g\parallel h$ and on opposite sides of the transversals.

Question 2

$\angle8$ and $\angle10$ are alternate exterior angles as they are outside the parallel - line sets and on opposite sides of the transversals.

Question 3

$\angle4$ and $\angle6$ are alternate interior angles because they are between the parallel lines $a\parallel b$ and on opposite sides of the transversal.

Question 4

$\angle11$ and $\angle13$ are consecutive/same - side interior angles since they are between the parallel lines $g\parallel h$ and on the same side of the transversal.

Question 5

$\angle3$ and $\angle5$ are supplementary because they are same - side interior angles for the parallel lines $a\parallel b$ and the transversal. The sum of same - side interior angles for parallel lines is $180^{\circ}$.

Question 6

$\angle6$ and $\angle8$ are vertical angles as they are opposite each other when two lines intersect.

Question 7

If $m\angle15 = 64^{\circ}$, $\angle15$ and $\angle10$ are corresponding angles for the parallel lines $g\parallel h$. Corresponding angles are congruent, so $m\angle10=64^{\circ}$.

Question 8

If $m\angle16 = 106^{\circ}$, $\angle16$ and $\angle10$ are same - side interior angles for the parallel lines $g\parallel h$. Since same - side interior angles are supplementary ($m\angle16 + m\angle10=180^{\circ}$), then $m\angle10 = 180 - 106=74^{\circ}$.

Question 9

$\angle1$ and $\angle2$ are vertical angles as they are opposite each other when two lines intersect.

Answer:

1. C. alternate exterior
2. C. alternate exterior
3. B. alternate interior
4. D. consecutive/same - side interior
5. C. supplementary
6. A. vertical angles
7. B. $64^{\circ}$
8. B. $74^{\circ}$
9. A. $\angle1$ and $\angle2$