Question

If the sides of a triangle are produced in order prove that the sum ofexterior angles so formed is equal to four right angles

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Answer 1

Explanation:

Let a, b, c be the measures of the interior angles and x, y, z be the measures of the exterior angles of the triangle. Where x and adjacent to a, y is adjacent to b and z is adjacent to c.

By interior angle sum postulate of a triangle:

a + b + c = 180°... (1)

Therefore, by remote interior angle theorem:

x = b + c.... (2)

y = a + c..... (3)

z = a + b.... (4)

Adding equations (2), (3) & (4)

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

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

x + y + z = 2(a + b + c)... (5)

From equations (1) & (5)

`x + y + z = 2 * 180 \degree \\ x + y + z = 360 \degree \\ x + y + z = 4 * 90\degree \\ x + y + z = 4 \: right \: angles`

Thus, the sum of exterior angles so formed is equal to four right angles.

Proved.