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

40. Alternate exterior angles

41. 108°

42. x = 4

43. x = 13

Step-by-step 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

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.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .