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Why is the sum of Angles in a Triangle Is 180 Degrees?

Why-is-the-sum-of-Angles-in-Triangle-Is-180-Degrees

You might have learnt that the sum of three angles in any triangle is 180 degrees. Do you know why for every triangle irrespective of its size and shape, the sum of angles is always 180 degrees?

To understand this, you should know what the measure of a straight angle is? You might have seen and used a protractor – an instrument to measure angles.

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Here you can see that if you start rotating a set of compasses by keeping its pointer at the center, from one end of a line segment to the other, you cover 180 degrees. Thus, the measure of the straight line is 180 degrees.

Now consider these two angles: 

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Here ∠1 + ∠2 = 1800

Therefore, ∠1 = 1800 – ∠2And, ∠2 = 1800 – ∠1

Now, we will move to a triangle ABC. The three angles of a triangle are ∠a, ∠b and ∠c.

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If you combine the three exterior angles, 1800 – ∠a, 1800 – ∠b and 1800 – ∠c, you get a full circle.

Since, measure of a full circle is 3600, therefore, 

(1800 – ∠a) + (1800 – ∠b) + (1800 – ∠c) = 3600

=> 1800 + 1800 + 1800 – ∠a – ∠b – ∠c = 3600

=> 5400 – (∠a + ∠b + ∠c) = 3600

=> ∠a + ∠b + ∠c = 5400 – 3600=> ∠a + ∠b + ∠c = 1800

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