Question

\small \angle L and \small \angle M are supplementary, \small m\angle L=12x+45 and \small m\angle M=18x-30. Determine the measure of each angle. \small m\angle L= degrees \small m\angle M= degrees

Answer 1

`L = 111`

`M = 69`

Explanation:

Given

`L = 12x + 45`

`M = 18x - 30`

Required

Determine L and M

Since both angles are supplementary;

`L + M = 180`

Substitute values for L and M

`12x + 45 + 18x - 30 = 180`

Collect Like Terms

`12x + 18x= 180 - 45 + 30`

`30x= 165`

Divide both sides by 30

`x = (165)/(30)`

`x = 5.5`

Substitute 5.5 for x in
`L = 12x + 45` and
`M = 18x - 30`

`L = 12 * 5.5 + 45`

`L = 111`

`M = 18 * 5.5 - 30`

`M = 69`