Question

Find the measure of x and y. State a reason for your solution.

Answer 1

• for x

`{ \tt{(4x - 2) \degree + 30 \degree = 68 \degree}} \\ { \rm{ \{alternate \: angles \}}} \\ \\ { \tt{4x + 28 = 68}} \\ { \tt{4x = 40}} \\ \\ { \boxed{ \boxed{{ \tt{ \: \: x = 10 \: \: }}}}}`

• for y:

`{ \tt{y + y + 68 + (4x - 2) + 30 = 360}} \\ { \rm{ \{angle \: sum \: of \: a \: circle \}}} \\ \\ { \tt{2y + 4x + 66 = 360}} \\ { \tt{2y + 4(10) + 66 = 360}} \\ { \tt{2y + 106 = 360}} \\ { \tt{2y = 254}} \\ \\ { \boxed{ \boxed{ \tt{ \: \: y = 127 \degree \: \: }}}}`

Answer 2

`x = 10 \\ y = 112`

Explanation:

Vertically opposite angles are equal

Therefore ,

`6 8 = 4x - 2 + 30`

Now solve for x

`68 - 30 = 4x - 2 \\ 38 = 4x - 2 \\ 38 + 2 = 4x \\ 40 = 4x \\ (40)/(4) = (4x)/(4) \\ 10 \degree = x`

Angles in a straight line is added up to 180°

Therefore,

`y + 68 = 180 \\ y = 180 - 68 \\ y =11 2 \degree`

Hope this helps you.

Let me know if you have any other questions :-)