math heelp please?

Question

AB (arrow on top of it) intersect CD (arrow on top of it) at E, m<AEC=3x, and m<AED=5x-60

a.findx

b.show that AB (arrow on top of it) is perpindicular to CD (arrow on top of it)

i mean an arrow like left and right

Answer 1

Favorite Answer

AEC+AED=180 (since, it is a straight line)

3x+5x-60=180

8x=240

x=30

AEC=3x=90

AED=5x-60=90

AB is perpendicular to CD

Answer 2

The two angles (AEC and AED) are supplementary angles - they share a common ray and are adjacent to each other on the same line (CED). Supplementary angles have a sum of 180 degrees. SO angles AEC and AED add up to 180.

3x + 5x - 60 = 180

8x - 60 = 180

8x = 240

x = 30

m<AEC = 3x = 3(30) = 90

m<AED = 5x - 60 = 5(30) - 60 = 150 - 60 = 90

The lines are perpendicular to each other because perpendicular lines form right (90 degrees) angles and they do!