Question

Q10. Prove that the sum of all the angles of a triangle is 180".
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Answer 1

Step-by-step explanation:

Given:- A triangle

Let us take a triangle ABC

To prove:-

sum of all the angles of a triangle is 180

Here , angle ABC +angle BCA +angle CAB =180

Construction:-

AM II BC

Proof:-

Now let us name angle ABC ,angle BCA , angle CAB as 1 , 2, 3

and angle MAB as 4 and another exterior angle as 5 (see in fig )

So, now 1= 4 (alternate interior angles)

5 = 2 (alternate interior angles)

Now we can take MA ray which is a straight line

So 4+3+5=180

Substituting 1 and 2 in place of 4 and 5 respectively

Therefore 1+2+3= 180

Therefore the sum of all the angles of a triangle is 180