line segments ab and cd intersect at o such that ac is parallel to db. If angle cab is 35 and angle cdb is 55 find angle bod

Answer:

Line segments ab and cd intersect each other at o. Line segment ac and db are parallal. So two traingles aoc and bod are formed.

So if line segment ac and db are parallal the line segments ab and cd will be transversal.

We also kwon that angle cab = 35^o and angle cdb = 55^o.

Since segment ac and db are parallal the line segments ab and cd will be transversal, then angle cab and angle abd are alternate interior angles.

As we know that when a transversal cuts two parallal lines the alternate interior angles are equal. So angle cab = angle abd = 35^o.

Since oac forms a triangle and the two angles of the triangle are known i.e. angle abd = 35^o and cdb = 55^o.

So as per angle sum property of triangle is equal to 180o, then

35 + 55 + angle bod = 180

angle bod = 180 - 90 = 90^o.

Ans: 90^o.