Question

40. Identify the special angle pair name for (angle)10 and (angle)6 .

41. Given l || m, m ( angle ) 2 = 72, find the m (angle) 3

42. Given l || m, m (angle) 9 = 9x + 5, and m (angle) 5 = 3x + 37, find the value of x.

43. Given m (angle)10 = 5x + 2, and m (angle) 6 = 3x + 28, find the value of x so that l || m

Answer 1

40. Alternate exterior angles

41. 108°

42. x = 4

43. x = 13

Explanation:

40. Given l || m, line n is transversal (intersects lines m and l), then angles 10 and 6 are alternate exterior angles.

41. Given l || m, line n is transversal (intersects lines m and l), then angles 2 and 3 are same side interior angles. Same side interior angles are supplementray (add up to 180°), so if m∠2=72°, then

m∠3=180°-72°=108°

42. Given l || m, line n is transversal (intersects lines m and l), then angles 10 and 6 are alternate interior angles. Alternate interior angles are congruent, so

`m\angle 9=m\angle 5\\ \\9x+5=x+37\\ \\9x-x=37-5\\ \\8x=32\\ \\x=4`

43. If alternate exterior angles 10 and 6 are congruent, then lines l and m are parallel. Find the value of x for which angles 10 and 6 are congruent.

`m\angle 10=m\angle 6\\ \\5x+2=3x+28\\ \\5x-3x=28-2\\ \\2x=26\\ \\x=13`