Question

The sides of a quadrilateral are produced in order to form exterior angles. Find the sum of
the exterior angles.
[Hint DAB+ Z1 = 180° (linear pair)--)
​

Answer 1

Answer :

360°

Solution :

Given,

The sides of a quadrilateral are produced in order to form exterior angles

The exterior angles are 1, 2, 3 and 4.

Let,

∠BAD = w°

∠ABC = x°

∠BCD = y°

∠CDA = z°

We know that,

Sum of all angles in a quadrilateral is 360°

⟶ w + x + y + z = 360°

As the sum of angles on straight line = 180° (linear pair),

∠1 + w = 180°

∠2 + x = 180°

∠3 + y = 180°

∠4 + z = 180°

Now, adding all the 4 equations,

1 + w + 2 + x + 3 + y + 4 + z = 180 + 180 + 180 + 180

1 + 2 + 3 + 4 + w + x + y + z = 720°

1 + 2 + 3 + 4 = 720 - (w + x + y + z)

1 + 2 + 3 + 4 = 720 - 360

1 + 2 + 3 + 4 = 360°

∴ Sum of exterior angles of quadrilateral = 360°

Answer 2

Answer:

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