Question

Show all work and explain in words

Findthe value of x. Then find the measure of each labeled angle.

Answer 1

Part 5)
`x=50\°`

Part 6)
`x=15\°`

Explanation:

Part 5) we know that

`(2x-10)\°+90\°=180\°` -----> by consecutive interior angles (supplementary angles)

solve for x

`2x=180\°-80\°`

`2x=100\°`

`x=50\°`

Find the value of the labeled angle

`(2x-10)\°=2(50\°)-10\°=90\°` ----> is a right angle

Verify the answer

we know that

In a quadrilateral the sum of the internal angles must be equal to 360 degrees

so

`(2x-10)\°+90\°+(180-x)\°+x\°=360\°`

`(2x+260)\°=360\°`

substitute the value of x

`2(50\°)+260\°=360\°`

`360\°=360\°` ------> is true, therefore the value of x is correct

Part 6) we know that

`(8x+10)\°+(4x-10)\°=180\°` -----> by consecutive interior angles (supplementary angles)

solve for x

`12x=180\°`

`x=15\°`

Find the value of each labeled angle

`(8x+10)\°=8(15\°)+10\°=130\°`

`(4x-10)\°=4(15\°)-10\°=50\°`

`130\°` and
`50\°` are supplementary angles