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 = 3c + 28, find the value of x so that l || m

Answer 1

40. Alternate exterior angles.

41.
`m\angle 3=108`.

42.
`x=4`

43.
`x=13`

Explanation:

Given:

From the figure, l and m are 2 lines and p and n are the transversals on the 2 lines.

Question 40:

[tex]m\angle 10\textrm{ and }m\angle 6[/tex] lie exterior to lines l and m are also alternate to each other. Therefore, they are called as a pair of alternate exterior angles.

Question 41:

If lines l || m, then the angles
`m\angle 2\textrm{ and }m\angle 3` are a pair of supplementary angles.

Therefore, the sum of angles 2 and 3 is equal to 180.

`m\angle 2+m\angle 3=180\\72+m\angle 3=180\\m\angle 3=180-72=108`

Therefore,
`m\angle 3=108`.

Question 42:

If lines l || m, then the angles
`m\angle 9\textrm{ and }m\angle 5` are a pair of alternate interior angles and equal to each other.

Therefore,
`m\angle 9=m\angle 5`

`9x+5=x+37\\9x-x=37-5\\8x=32\\x=(32)/(8)=4`

Therefore,
`x=4`.

Question 43:

If lines l || m, then the angles
`m\angle 10\textrm{ and }m\angle 6` are a pair of alternate exterior angles and equal to each other.

Therefore,
`m\angle 10=m\angle 6`

`5x+2=3x+28\\5x-3x=28-2\\2x=26\\x=(26)/(2)=13`

Therefore,
`x=13`.