# prove that the sum of the angles of a triangle is 180 degree

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## Prove that the sum of angles of a triangle is 180.

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## Prove that the sum of angles of a triangle is 180.

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Updated on : 2022-09-05

Solution Verified by Toppr

Step -1: Prove that the sum of angles of a triangle is 180

∘ .

Let a triangle ABC and draw a line l through A and parallel to the base BC.

∵BC∥l and AB and AC are transversals on it.

∴∠4=∠2…(i) (Alternate angles)

and ∠5=∠3…(ii) (Alternate angles)

Adding equations (i) and (ii), we get

∠4+∠5=∠2+∠3

Add ∠1 on both sides.

⇒∠1+∠4+∠5=∠1+∠2+∠3…(iii)

∠1+∠4+∠5=180 ∘

(∵l is a straight line)

From (iii), ∠1+∠2+∠3=180 ∘

Hence, sum of angles of a triangle is 180

∘ . Hence Proved.

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## Prove that sum of angles of triangle is 180 degree.

Prove that sum of angles of triangle is 180 degree.

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Prove that sum of angles of triangle is 180 degree.

Question

Prove that sum of angles of triangle is

180 degree. Open in App Solution

**To prove:**

The sum of angles of triangle is

180 degree.

**Proof:**

Lets take a triangle

△ A B C Consider base B C , draw a line M N , parallel to B C

Now, A B & A C

will out as transversals.

In figure, A B is transversal, and M N ∥ B C ⇒ ∠ 2 = ∠ 4

[Since, alternate interior angles]--(1)

A C is transversal, and M N ∥ B C ⇒ ∠ 3 = ∠ 5

[Since, alternate interior angles]--(2)

Adding equation(i) and (ii), we get

∠ 2 + ∠ 3 = ∠ 4 + ∠ 5 Adding ∠ 1

on both sides, we get

⇒ ∠ 1 + ∠ 2 + ∠ 3 = ∠ 1 + ∠ 4 + ∠ 5 .....(iii) Since, ∠ 4 + ∠ 1 + ∠ 5

will form a linear pair.

As we know that the some of angles of a linear pair is

180 ∘ ⇒ ∠ 4 + ∠ 1 + ∠ 5 = 180 ∘

Substitute above equation in equation(iii), we get

⇒ ∠ 2 + ∠ 1 + ∠ 3 = 180 ∘ i.e., in △ A B C , ∠ A + ∠ B + ∠ C = 180 ∘ Hence, proved. Suggest Corrections 78

SIMILAR QUESTIONS

**Q.**Prove that the sum of all interior angles of a triangle is 180°.

**Q.**Prove that the sum of angles of a triangle is 180.

**Q.**Prove that sum of all angles of triangle is

180 0 .

**Q.**Prove that the sum of the angles of the triangle is

180 ∘ .

**Q.**Prove that sum of all angles of a triangle is

180 ∘ . View More

## The angle sum of a Triangle is 180°

This lesson lets students find (by measuring) that angle sum in a triangle is 180°. The lesson also contains a simple proof of this fact and varied exercises.

## The angle sum of a Triangle is 180° - lesson with proof & varied exercises

1. Draw ANY triangle you like here.

(Use a ruler!) Measure all its

angles. Calculate the angle sum.

It is ______°.

2. Draw another triangle here.

Measure all its angles.

Calculate the angle sum.

It is ______°.

Above, you probably made a guess that the sum of the angles in a triangle is 180°.

That is true. Here is a for it. Proof means that we use already established principles to prove

that some new statement is always true. See if you can understand the reasoning in this proof!

We draw a line parallel to AB that passes

through point C.

Angles C and C' are vertical angles,

therefore ∠C = ∠C'.

Angles B and B' are corresponding angles,

therefore ∠B = ∠B'.

Angles A and A' are corresponding angles, therefore ∠A = ∠A'.

So, the angle sum ∠A + ∠B + ∠C is equal to the angle sum ∠A' + ∠B' + ∠C'.

The three angles A', B', and C' form together a straight angle (they are along the line ).

So, their angle sum is 180°. But then the angle sum ∠A + ∠B + ∠C must also be 180°.

3. Calculate the angle marked with the question mark. .

**a.**

**b.**

**c.**

4. A certain triangle has three equal angles.

What is the measure of each angle? _______°

Draw one using your protractor.

Make each of its sides 5 cm long.

This triangle has a special name.

What is it?

5. Can you draw a triangle that has

two obtuse angles? Why or why not?

6. **a. **Draw a triangle with 65° and 50° angles, with

a 7.5-cm side between those two angles.

Start out by drawing the 7.5-cm side.

**b.**the third angle. It is _______°.

Then measure from your triangle to check.

**c.**Classify your triangle according to its

sides and angles:

It is _________________________

and _________________________.

Calculate the angle marked with “?”.

**Math Mammoth Geometry 1**

A self-teaching worktext for 4th-5th grade that covers angles, triangles, quadrilaterals, cirlce, symmetry, perimeter, area, and volume. Lots of drawing exercises!

**Download ($6.90)**. Also available as a printed copy.

=> Learn more and see the free samples!

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