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.
