Question

If the side BC of Δ ABC is produced on both sides, then write the difference between the sum of the exterior angles so formed and ∠A.

Answer 1

The difference between the sum of the exterior angles so formed and ∠A is 180°.

Explanation:

Given that

BC produced on both sides  .

Sum of the interior angles of the triangle = 180°

$\angle \mathrm{A}+\angle \mathrm{ABC}+\angle \mathrm{ACB}=180^{\circ}$ – – – (1)

By exterior angle theorem,

Exterior angle is equal to the sum of the opposite interior angles.

$\angle \mathrm{ABD}=\angle \mathrm{A}+\angle \mathrm{ACB}$ – – – (2)

$\angle \mathrm{ACE}=\angle \mathrm{A}+\angle \mathrm{ABC}$ – – – (3)

Adding (2) and (3),

$\angle \mathrm{ABD}+\angle \mathrm{ACE}=\angle \mathrm{A}+(\angle \mathrm{A}+\angle \mathrm{ACB}+\angle \mathrm{ABC})$

$\angle \mathrm{ABD}+\angle \mathrm{ACE}=\angle \mathrm{A}+180^{\circ}$  (using (1))

$(\angle A B D+\angle A C E)-\angle A=180^{\circ}$

The difference between the sum of the exterior angles so formed and ∠A is 180°.

To learn more...

1. The side BC of triangle ABC is produced on both sides prove that the sum of the exterior angles so formed is greater than angle A by two right angles

https://brainly.in/question/2006544

2. The side BC of triangle ABC is produced on both sides prove that the sum of two exterior angle so formed is greater than angle a by 180°

https://brainly.in/question/4622933