Question

Please, I need assistance, thank you!

Answer 1

a.
`x=45`

b. The lines
`AD` and
`BC` would be parallel.

Explanation:

a) By definition,the sum of the interior angles of a quadrilateral is 360 degrees.

Notice that the quadrilateral has an angle of 90 degrees. Then, you can write the following equation:

`x+2x+3x+90=360`

Solving for "x", you get:

`6x=360-90\\\\x=(270)/(6)\\\\x=45`

b) Knowing the value of "x", you know the measure of the angles of the quadrilateral:

`\angle A=2x=2(45)=90\°\\\\\angle B=90\°\\\\\angle C=x=45\°\\\\\angle D=3x=3(45)=135\°`

Since:

`\angle A` ≅
`\angle B`

When
`ABCD` is drawn to scale, the lines
`AD` and
`BC` would be parallel.