Question

In Fig, the sides BC, CA and BA of a △ABC have been produced to D, E and F respectively. If ∠ACD = 105° and ∠EAF = 45°; find all the angles of the △ABC.

Answer 1

In a △ABC, ∠BAC and ∠EAF are vertically opposite angles.

Hence, we can write as

∠BAC = ∠EAF = 45°

Considering the exterior angle property, we have

∠BAC + ∠ABC = ∠ACD = 105°

On rearranging we get

∠ABC = 105°– 45° = 60°

We know that the sum of angles in a triangle is 180°

∠ABC + ∠ACS +∠BAC = 180°

∠ACB = 75°

Therefore, the angles are 45°, 65° and 75°.