Question

lines m and p are cut by the transversal n. determine the value of x. write the measures of the six angles. show all work

Answer 1

x = 36°

m<1 = 36°

m<2 = 144°

m<3 = 36°

m<4 = 144°

m<5 = 144°

m<6 = 36°

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°