Question

ABCD is a quadrilateral.

a) Calculate the value of x.
b) When ABCD is drawn to scale, would
the lines AD and BC be parallel or not? Yes/No
Diagram not drawn to scale
You must justify your answer without
using a scale drawing.

Answer 1

a) x=45°

b) yes because both ∠DAB and ∠ABC are perpendicular to the same line segment, they most be parallel.

Explanation:

a) all quadrilaterals have internal angels that add up to 360°

So ∠DAB + ∠ABC + ∠BCD + ∠CDA = 360°. Substituting each ∠ with its given value gives:

2x°+90°+x°+3x°=360°

Simplifying:

-> 90°+6x=360°

Subtracting 90°:

-> 6x=270°

Dividing by 6:

-> x=45°

Substituing back:

∠DAB=2x=2*45°=90°

∠ABC=90°

∠BCD=x=45°

∠CDA=3x=3(45)=135°

b) Yes because both ∠DAB and ∠ABC intersect the line segment AB at 90° angles/both ∠DAB and ∠ABC are perpendicular to the line segment AB. Because both ∠DAB and ∠ABC are perpendicular to the same line segment, they most be parallel.