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) 1)__ a. corresponding b. alternate interior c. alternate exterior d. consecutive/same - side interior 2) the special angle - pair name for ∠8 and ∠10 is (g6a) 2) a. corresponding b. alternate interior c. alternate exterior d. consecutive/same - side interior 3) the special angle - pair name for ∠4 and ∠6 is (g6a) 3) a. corresponding b. alternate interior c. alternate exterior d. consecutive/same - side interior 4) the special angle - pair name for ∠11 and ∠13 is (g6a) 4) a. corresponding b. alternate interior c. alternate exterior d. consecutive/same - side interior 5) ∠3 and ∠5 are (g6a) 5) a. congruent b. complementary c. supplementary d. bisected 6) ∠6 and ∠8 are (g6a) 6) a. vertical angles b. complementary angles c. linear pair d. corresponding angles 7) if m∠15 = 64°, then the measure of m∠10 is (g6a) 7) a. 26° b. 64° c. 32° d. 116° 8) if m∠16 = 106°, then the measure of m∠10 is (g6a) 8) a. 106° b. 74° c. 53° d. 16° 9) which is a pair of vertical angles? (g6a) 9)__ 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 two parallel lines and on opposite sides of the transversal. Alternate exterior angles are outside the two parallel lines and on opposite sides of the transversal. Consecutive/same - side interior angles are between the two parallel lines and on the same side of the transversal. Vertical angles are opposite each other when two lines intersect.

Step2: Analyze each angle - pair

1. ∠1 and ∠14 are alternate exterior angles.
2. ∠8 and ∠10 are alternate interior angles.
3. ∠4 and ∠6 are alternate interior angles.
4. ∠11 and ∠13 are consecutive/same - side interior angles.
5. ∠3 and ∠5 are supplementary (they form a linear pair, and the sum of angles in a linear pair is 180°).
6. ∠6 and ∠8 are vertical angles.
7. If ∠15 = 64°, and ∠15 and ∠10 are corresponding angles, then ∠10=64°.
8. If ∠16 = 106°, and ∠16 and ∠10 are supplementary (linear - pair relationship), then ∠10 = 180°−106° = 74°.
9. ∠1 and ∠2 are a pair of vertical angles.

Answer:

1. c. alternate exterior
2. b. alternate interior
3. b. alternate interior
4. d. consecutive/same - side interior
5. c. supplementary
6. a. vertical angles
7. b. 64°
8. b. 74°
9. a. ∠1 and ∠2