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CBSE Class 9 Answered

If the sides of a triangle are produced in order, prove that the sum of the exterior angles so formed is equal to four right angles.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer

In the figure, by exterior angle property, you have

ACD = A+ B
CBF = A+ C
BAE = B+ C
Adding the above equations, you get
ACD +CBF +BAE = A+ B +A+ C + B+ C
                                            = 2 (A+ B +C)
                                            = 2 180o      (angle sum of a )
ACD +CBF +BAE =360o
That is the sum of the exterior angles = four right angles. (360o = 490o)
Answered by | 04 Jun, 2014, 03:23: PM

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