Question

Please, I need assistance, thank you!

Answer 1

Answer:

a. $x=45$

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

Step-by-step 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:

$6x=360-90\\\\x=\frac{270}{6}\\\\x=45$

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.