Question

Find x
and
each of the
interior angles.​

Answer 1

Part 1)
`x=27`

Part 2) The measure of the interior angles are 64°-67°-49°

Explanation:

see the attached figure to better understand the problem

step 1

Find the value of x

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

In this problem

`(3x-17)^o+(x+40)^o+(2x-5)^o=180^o`

Solve for x

Combine like terms

`(6x+18)^o=180^o`

Subtract 18 both sides

`6x=180-18`

`6x=162`

Divide by 6 both sides

`x=27`

step 2

Find the measure of each interior angle

substitute the value of x in each measure

`(3(27)-17)=64^o`

`(27+40)=67^o`

`(2(27)-5)=49^o`