Question

Please tell me the answer.

Answer 1

-The measure of
`\angle A` :

`\angle A = 144\textdegree`

-The measure of
`\angle B` (if needed):

`\angle B = 144\textdegree`

Explanation:

-Set the measure of
`\angle A` on one side and set the measure of
`\angle B` on the other side and it will be written as:

`10x + 24 = 6x + 72`

-Then, solve for
`x` :

`10x + 24 = 6x + 72`

`10x + 24 - 6x = 6x - 6x + 72`

`4x + 24 = 72`

`4x + 24 - 24 = 72 - 24`

`4x = 48`

`(4x)/(4) = (48)/(4)`

`x = 12`

-After you have found the value of
`x`, plug in both the measure of
`\angle A` and
`\angle B` in order to get the actual angle measurement of
`\angle A` and
`\angle B` :

Finding the measure of
`\angle A` :

`\angle A = 10(12) + 24`

`\angle A = 120 + 24`

`\angle A = 144\textdegree`

Finding the measure of
`\angle B` :

`\angle B = 6(12) + 72`

`\angle B = 72 + 72`

`\angle B = 144\textdegree`

-Notice: That reason why both
`\angle A` and
`\angle B` have the same measurements, its because they are Alternate Exterior Angles, based on the diagram shown.