Rukmini has a farm land which is triangular in shape.What is the sum of all the exterior angles taken in an order of the farm land?（ ）

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Rukmini has a farm land which is triangular in shape.What is the sum of all the exterior angles taken in an order of the farm land?（ ）

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Let \(ABC\) be a triangle.

Measure of exterior angle adjacent to \(\angle A=180^{\circ}-\angle A\).

Measure of exterior angle adjacent to \(\angle B=180^{\circ}-\angle B\).

Measure of exterior angle adjacent to \(\angle C=180^{\circ}-\angle C\).

Measure of exterior angles\(=180^{\circ}-\angle A+180^{\circ}-\angle B+180^{\circ}-\angle C\)

\(=540^{\circ}-(\angle A+\angle B+\angle C)\)

\(=540^{\circ}-180^{\circ}\) [Sum of all angles of a triangle is \(180^{\circ}\)].

\(=360^{\circ}\).

So, sum of all the exterior angles taken in an order of the farm land is \(360^{\circ}\).

Measure of exterior angle adjacent to \(\angle A=180^{\circ}-\angle A\).

Measure of exterior angle adjacent to \(\angle B=180^{\circ}-\angle B\).

Measure of exterior angle adjacent to \(\angle C=180^{\circ}-\angle C\).

Measure of exterior angles\(=180^{\circ}-\angle A+180^{\circ}-\angle B+180^{\circ}-\angle C\)

\(=540^{\circ}-(\angle A+\angle B+\angle C)\)

\(=540^{\circ}-180^{\circ}\) [Sum of all angles of a triangle is \(180^{\circ}\)].

\(=360^{\circ}\).

So, sum of all the exterior angles taken in an order of the farm land is \(360^{\circ}\).

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