Q. 84.2( 6 Votes )

If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is
A. 90°

B. 180°

C. 270°

D. 360°

Answer :

Let, ABC be a triangle and AB, BC and AC produced to D, E and F respectively.

A + B + C = 180o (i)

CBD = C + A (Exterior angle theorem) (ii)

ACE = A + B (Exterior angle theorem) (iii)

BAF = B + C (Exterior angle theorem) (iv)

Adding (ii), (iii) and (iv) we get

CBD + ACE + BAF = 2A + 2B + 2C

CBD + ACE + BAF = 2 (A + B + C)

CBD + ACE + BAF = 2 * 180o

CBD + ACE + BAF = 360o

Thus, sum of all three exterior angles is 360o.

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