Answer:
a. [tex]x=45[/tex]
b. The lines [tex]AD[/tex] and [tex]BC[/tex] 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:
[tex]x+2x+3x+90=360[/tex]
Solving for "x", you get:
[tex]6x=360-90\\\\x=\frac{270}{6}\\\\x=45[/tex]
b) Knowing the value of "x", you know the measure of the angles of the quadrilateral:
[tex]\angle A=2x=2(45)=90\°\\\\\angle B=90\°\\\\\angle C=x=45\°\\\\\angle D=3x=3(45)=135\°[/tex]
Since:
[tex]\angle A[/tex] ≅ [tex]\angle B[/tex]
When [tex]ABCD[/tex] is drawn to scale, the lines [tex]AD[/tex] and [tex]BC[/tex] would be parallel.
