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
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 \(360^{\circ}\).
Rajan borrowed Rs. \(1050\) from his friend at \(8\%\) p.a. simple interest for \(4\) years. After \(4\) years he paid Rs. \(1386\) and settled the account. Simple interest paid by Rajan is( )