Question

Please answer and explain how you did it.

Answer 1

Refer to the attached image.

Given:
`m \angle A = 65^\circ` and measure of exterior angle at C =
`117^\circ`.

We have to determine the measure of angle B and angle BCA.

By applying exterior angle property of the triangle which states:

"An exterior angle of a triangle is equal to the sum of the opposite interior angles".

So, exterior angle C =
`m \angle A + m \angle B`

`117^\circ = 65^\circ+ m \angle B`

`m \angle B = 52^\circ`

Now, applying angle sum property in triangle ABC which states:

"The sum of all the angles of a triangle is 180 degrees".

`m \angle A + m \angle B + m \angle BCA = 180^\circ`

`65^\circ + 52^\circ + m \angle BCA = 180^\circ`

`117^\circ + m \angle BCA = 180^\circ`

`m \angle BCA = 180^\circ - 117^\circ`

`m \angle BCA =63^\circ`

Therefore, the measure of
`m \angle B = 52^\circ` and
`m \angle BCA =63^\circ`.