Question

In the figure, find the values of x and y hence show that $AB\parallel CD$. [3 MARKS]​

Answer 1

Concept: 1.5 Marks
Application: 1.5 Marks

$\angle AEG+\angle AEH={180}^{\circ }$ (Linear pair of angles)

${50}^{\circ }+x={180}^{\circ }$

$x={180}^{\circ }-{50}^{\circ }={130}^{\circ }$ ...(i)

$y={130}^{\circ }$ ...(ii) (Vertically opposite angles)

$x={130}^{\circ }$ and $y={130}^{\circ }$

From (i) and (ii), x = y

But these are alternate interior angles and they are equal.

So,we can say that $AB\parallel CD$.