Question

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

Answer 1

Answer:

40. Alternate exterior angles.

41. $m\angle 3=108$.

42. $x=4$

43. $x=13$

Step-by-step 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, $m\angle 9=m\angle 5$

$9x+5=x+37\\9x-x=37-5\\8x=32\\x=\frac{32}{8}=4$

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, $m\angle 10=m\angle 6$

$5x+2=3x+28\\5x-3x=28-2\\2x=26\\x=\frac{26}{2}=13$

Therefore, $x=13$.