Question

LAST ONE \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

Answer 1

`m\angle L = 111\degree \\</p><p>m\angle M = 69\degree`

Explanation:

Since, angle L and angle M are supplementary.

`\therefore m\angle L + m\angle M= 180\degree \\ \therefore \: 12x + 45 + 18x - 30 = 180 \degree \\ \therefore \: 30x + 15= 180 \degree\\ \therefore \: 30x= 180 \degree - 15 \degree\\ \therefore \: 30x= 165 \degree \\ x = (165 \degree)/(30) \\ x = 5.5 \degree \\ \\ m\angle L = 12x + 45 \\ m\angle L = 12 * 5.5 + 45 \\ m\angle L = 66 + 45 \\ \huge \red{ \boxed{ m\angle L = 111 \degree}} \\ \\ m\angle M=18x - 30 \\ m\angle M=18 * 5.5 - 30 \\ m\angle M=99 - 30 \\ \huge \purple{ \boxed{ m\angle M=69 \degree}} \\`