Question

What is the answer?

Answer 1

Part A

The 4 angles of a quadrilateral add to 360. To see why, draw a line from A to C. The quadrilateral is divided into 2 triangles. All triangles have interior angles that add to 180. Since there are 2 such triangles, the total is 2*180 = 360. Write a summation for the 4 angles.

2x + 3x + x + 90 = 360     Combine like terms on the left

6x + 90 = 360                   Subtract 90 from both sides.

6x + 90 - 90 = 360 - 90   Collect like terms

6x = 270                            Divide both sides by 6

6x/6 = 270/6                     Do the division

x = 45

Part B

Since x = 45 then2x = 90

Since <A and <B = 90 And since they are equal interior  angles and

both are 90 degrees,the lines are parallel.