Question

in the quadrilateral abcd in which ab is parallel to dc angle dab=120 degree and angle abc=110 degree find the measure of angle c and angle d

Answer 1

Lets extend the dc to e on the left and to f on the right.

We will have line ef with points d and c on it.

Now, given that ab is parallel to dc and da and cb cut across the two parallel lines, we will use the concept of alternate angles.

From the extended figure using the concept of alternate angles :

Angle cba is equal to angle bcf = 110°

Note : Alternate angles are equal.

Angle bcf and bcd lie on a straight line and angles on a straight line, add up to 180°.

The angle bcd is thus 180 - 110 = 70°.

Angle ade is also alternate to dab

ade = dab = 120°

Therefore angle adc lies on a straight line with ade and hence :

adc =180 - 120 = 60°