If all three sides of a triangle are produced in an order then prove that sum of all three exterior angle is 360°
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Let a ∆ABC
let angle(BAC) = x
angle(ABC) = y
angle(ACB) = z
so its exterior angle would be 180°-x, 180°-y, 180°- z
As we know that the sum of angles of a traingle is 180°
so x+y+z = 180° ......(1)
The sum of exterior angles will be
= 180°-x + 180°-y + 180°-z
= 540° - (x+y+z)
= 540° - 180° ( from (1))
= 360°
Hence Proved
let angle(BAC) = x
angle(ABC) = y
angle(ACB) = z
so its exterior angle would be 180°-x, 180°-y, 180°- z
As we know that the sum of angles of a traingle is 180°
so x+y+z = 180° ......(1)
The sum of exterior angles will be
= 180°-x + 180°-y + 180°-z
= 540° - (x+y+z)
= 540° - 180° ( from (1))
= 360°
Hence Proved
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