Question

In triangle ABC, ∠ABC=140°, BC>AB, D is a point on BC such that AB=BD, AD=DC, ACB=? (in degrees)

Answer 1

Answer:

We know that if a line through one of the vertex of a triangle divides the opposite side in the ratio of the other two sides, the line bisects the angle at the vertex.

So in the given equation,

AC

AB

=

CD

BD

⇒AD bisects ∠A.

∠A=180

∘

−(70

∘

+50

∘

) (Sum of angles of a triangle =180

∘

)

∴∠BAD=

2

∠A

=

2

60

∘

=30

∘