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 $m \angle BCA =63^\circ$.