Question

In the diagram shown, line m is parallel to line n. They are crossed by transversals r and s. Finally, r and s are perpendicular to each other. It is known that angle ABE=126° as shown.(a) What is measure of angle DEB? Justify.(b) What is measure of angle DEC? Justify.

Answer 1

From the diagram;

a}

Angle ABE = 126°

Angle EBC = 180° - 126° = 54° -----------supplimentary angles add up to 180°

So angle DEB=EBC = 54° -------Alternate angles

b} Angle DEC will be:

< BEF = 126°

< BEC = 90° ----------ray x is a perpendicular bisector of ray r

So,144°