Question

prove that the sum of three exterior angle of a triangle formed by producing the sides in order angle is 4 angle or 360 degree​

Answer 1

To prove:

The sum of three exterior angle of a triangle formed by producing the sides in order angle is 4 right angles or 360°.

Proof:

Let ABC is a triangle.

In Δ ABC,

• x, y and x are exterior angles.
• a, b and c are interior angles.

As we know that the exterior angle of a triangle are equal to the sum of the two opposite interior angles, therefore-

• x = b+c
• y = a+c
• z = a+b

So,

x+y+z = (b+c)+(a+c)+(a+b)

or, x+y+z = b+c+a+c+a+b

or, x+y+z = a+a+b+b+c+c

or, x+y+z = 2a+2b+2c

or, x+y+z = 2(a+b+c)

As we know that the sum of all interior angles of a triangle is 180°, therefore-

x+y+z = 2(a+b+c)

or, x+y+z = 2(180)

or, x+y+z = 2×180

or, x+y+z = 360

So, x+y+z = 360° = 4 right angles

Proved:

The sum of three exterior angle of a triangle formed by producing the sides in order angle is 4 right angles or 360°.

Hope this helps you to get to your answer.

Answer 2

Answer:

In ABC , By Angle sum property of triangle,

ABC + BAC + BC A =180°-------(1)

Now, By linear pair property

1 + BAC = 180° ---------(2)

And 2 + ABC = 180° ---------(3)

And 3 + BCA = 180° ---------(4)Add equation (2) (3) and (4)

1 +BAC+2+ABC+3+BCA= 180°+180°+180°

1+2 +3 + BAC+ABC+BCA = 540°

1+2 +3 + 180° = 540° (from eq 1)

1+2 +3 = 540° - 180°

1+2 +3 = 360°

Hence, it is proved that sum exterior angle of triangle is 360°