Question

In the figure, the sides BC, CA. BA of a triangle ABC are produced to D, E, F respectively, Find the angles of the triangle ABC​

Answer 1

Step-by-step explanation:

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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°.

Answer 2

Answer : 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°.