Question

Pls write the steps u did​

Answer 1

When two parallel lines are intersected by a transversal, the same-side exterior angles are supplementary. That means that their sum is 180.

Using that logic, if the two roads were parallel, then the sum of their same-side exterior angles will add up to 180. Yet their same-side exterior angles add up to 170 (130 + 40 = 170), hence they can't be parallel.

See the drawing attached below.

Using supplmenatry angles (two angles whose sum of measures add up to 180 or a straight line), we can say that:

m<DIE + m<HID = 18

40 + m<HID = 180

m<HID = 140

Similarly:

m<BHC + m<CHI = 180

130 + m<CHI = 180

m<CHI = 50

Using verticle angles therome, (when two lines intersect, the angles opposite to eachother are congruent, or have the same measure), we can say that:

m<DIE = m<GIH = 40

m<GIE = m<HID = 140

m<CHI = m<AHB = 50

m<BHC = m<AHI = 130