Answer:
40. Alternate exterior angles.
41. [tex]m\angle 3=108[/tex].
42. [tex]x=4[/tex]
43. [tex]x=13[/tex]
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 [tex]m\angle 2\textrm{ and }m\angle 3[/tex] are a pair of supplementary angles.
Therefore, the sum of angles 2 and 3 is equal to 180.
[tex]m\angle 2+m\angle 3=180\\72+m\angle 3=180\\m\angle 3=180-72=108[/tex]
Therefore, [tex]m\angle 3=108[/tex].
Question 42:
If lines l || m, then the angles [tex]m\angle 9\textrm{ and }m\angle 5[/tex] are a pair of alternate interior angles and equal to each other.
Therefore, [tex]m\angle 9=m\angle 5[/tex]
[tex]9x+5=x+37\\9x-x=37-5\\8x=32\\x=\frac{32}{8}=4[/tex]
Therefore, [tex]x=4[/tex].
Question 43:
If lines l || m, then the angles [tex]m\angle 10\textrm{ and }m\angle 6[/tex] are a pair of alternate exterior angles and equal to each other.
Therefore, [tex]m\angle 10=m\angle 6[/tex]
[tex]5x+2=3x+28\\5x-3x=28-2\\2x=26\\x=\frac{26}{2}=13[/tex]
Therefore, [tex]x=13[/tex].
