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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?（ ）
A. $$90^{\circ }$$
B. $$180^{\circ }$$
C. $$360^{\circ }$$
D. Can not be determined
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## QuestionMathsClass 8

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?（ ）
A. $$90^{\circ }$$
B. $$180^{\circ }$$
C. $$360^{\circ }$$
D. Can not be determined

C
4.6
4.6

## 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 $$360^{\circ}$$.