Question

In a triangle ABC, if AB = AC and AB is produced to D such that BD = BC, find ∠ACD: ∠ADC.

Answer 1

In the given ,and AB is produced to D such that

We need to find

Now, using the property, “angles opposite to equal sides are equal”

As

........(1)

Similarly,

As

........(2)

Also, using the property, “an exterior angle of the triangle is equal to the sum of the two opposite interior angle”

In ΔBDC

(Using 2)

From (1), we get

.......(3)

Now, we need to find

That is,

(Using 3)

(Using 2)

Eliminating from both the sides, we get 3:1

Thus, the ratio of is