Question

The three lines shown in the diagram below intersect at the same point. The measures of some of the

angles in degrees are given as...

Answer 1

x =16, y = 151.2

Explanation:

Since angle 3/5y and angle 12 and angle 42 lies on the same straight line,

`(3)/(5) y + 12 + 42 = 180 \\ (3)/(5) y = 180 - 12 - 42 \\ (3)/(5) y = 180 - 54 \\ (3)/(5) y = 126 \\ y = 126 / (3)/(5) \\ = 126 * (5)/(3) \\ = 151.2`

Since angle 3(x-2) , 3/5y and 12 lies on the same straight line and we know what y is,

`3(x - 2) + (3)/(5) y + 12 = 180 \\ 3(x - 2) + (3)/(5) (151.2) + 12 = 180 \\ 3(x - 2) + 126 + 12 = 180 \\ 3(x - 2) = 180 - 12 6 - 12 \\ 3(x - 2) = 42 \\ x - 2 = (42)/(3) \\ x = 14 + 2 \\ =16`