Answer:
x = 36°
m<1 = 36°
m<2 = 144°
m<3 = 36°
m<4 = 144°
m<5 = 144°
m<6 = 36°
Step-by-step explanation:
✔️x° + 4x° = 180° (linear angle pair theorem)
5x = 180
x = 180/5
x = 36°
For easy identification, the six angles to be found have been labelled <1 to <6 as shown in the attachment below.
✔️m<1 = x° (vertical angles pair)
m<1 = 36° (substitution)
✔️m<2 = 4x° (vertical angles pair)
Plug in the value of x
m<2 = 4(36)
m<2 = 144°
✔️m<3 = x° (alternate interior angles theorem)
m<3 = 36° (substitution)
✔️m<4 = 4x° (corresponding angles theorem)
m<4 = 4(36) (substitution)
m<4 = 144°
✔️m<5 = 4x° (alternate exterior angles theorem)
m<5 = 4(36)
m<5 = 144°
✔️m<6 = x° (corresponding angles theorem)
m<6 = 36°
