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

Answer:

x =16, y = 151.2

Step-by-step explanation:

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

$\frac{3}{5} y + 12 + 42 = 180 \\ \frac{3}{5} y = 180 - 12 - 42 \\ \frac{3}{5} y = 180 - 54 \\ \frac{3}{5} y = 126 \\ y = 126 \div \frac{3}{5} \\ = 126 \times \frac{5}{3} \\ = 151.2$

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

$3(x - 2) + \frac{3}{5} y + 12 = 180 \\ 3(x - 2) + \frac{3}{5} (151.2) + 12 = 180 \\ 3(x - 2) + 126 + 12 = 180 \\ 3(x - 2) = 180 - 12 6 - 12 \\ 3(x - 2) = 42 \\ x - 2 = \frac{42}{3} \\ x = 14 + 2 \\ =16$