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?（ ）
Answer
C
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Solution
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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