Question

If the side of a triangle are produced in order , prove that angle x + angle y + angle Z is equal to four right angles.


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Answer 1

ANSWER:-

Given:

If the side of a triangle are produced in order.

To prove:

Prove that ∠x + ∠y+ ∠z is equal to four right angles.

Solution:

Let ∆ABC in which A=1, B=2 & C=3

Let the exterior angle of A, B & C be ∠x,∠y & ∠z respectively.

So,

We know that sum of angles of a ∆= 180°.

From Above attachment a figure;

∠1 + ∠x = 180° [linear pair].....(1)

∠2 + ∠y = 180° [linear pair].....(2)

∠3 + ∠z = 180° [linear pair].....(3)

Adding the equation, we get;

∠1+∠x+∠2+∠y+∠3+∠z=180°+180°+180°

=)(∠1+∠2+∠3)+∠x+∠y+∠z= 540°

=) 180° + ∠x + ∠y + ∠z= 540°

=) ∠x + ∠y + ∠z= 540° - 180°

=) ∠x + ∠y+ ∠z= 360°

So,

The sum of the exterior angle of a ∆ is 360°.

Hence,

∠x + ∠y + ∠z= 4 × 90° [4×right angle]

Proved.

Hope it helps ☺️