Question

Sum of measures of exterior angles of a polygon is???​

Answer 1

Answer:

Here is your answer

Step-by-step explanation:

We know that, exterior angle + interior adjacent angle = 180°

So, if the polygon has n sides, then

Sum of all exterior angles + Sum of all interior angles = n × 180°

So, sum of all exterior angles = n × 180° - Sum of all interior angles

Sum of all exterior angles = n × 180° - (n -2) × 180°

                                     = n × 180° - n × 180° + 2 × 180°

                                     = 180°n - 180°n + 360°

                                     = 360°

Therefore, we conclude that sum of all exterior angles of the polygon having n sides = 360°

Answer 2

Solution :-

Let us assume that, a polygon have total n sides .

we know that,

• Exterior angle + Interior angle = 180° (Linear pair)

So,

→ Sum of Exterior angles + Sum of Interior angle = Sum of linear pair angles .

→ Sum of Exterior angles = Sum of linear pair angles - Sum of Interior angle -------- Eqn.(1)

also,

→ Sum of linear pair angles with n sides = 180° * n

→ Interior angles of a polygon with n sides = (n - 2) * 180° .

then, putting both values in Eqn.(1) we get,

→ Sum of Exterior angles = 180° * n - (n - 2) * 180°

→ Sum of Exterior angles = 180° * n - (180° * n - 360°)

→ Sum of Exterior angles = 180° * n - 180° * n + 360°

→ Sum of Exterior angles = 360° (Ans.)

Hence, we can conclude that, the sum of measures of exterior angles of a polygon is equal to 360°.

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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