# Can you explain me the angle sum property of a triangle ?

Consider a triangle PQR in which 1, 2 and 3 are the angles of Δ PQR (figure shown below). Angle sum property of a triangle says that sum of the three angles in a triangle is 180 degrees, i.e.,

1 + 2 + 3 = 1800. We will now see the proof of the above statement.

We use the properties related to parallel lines to prove this. For this, let us draw a line XPY parallel to QR through the opposite vertex P, as shown in the figure given below Now, XPY is a line.

Therefore, 4 + 1 + 5 = 1800 … (1)

But XPY || QR and PQ, PR are transversals.

So, 4 = 2 and 5 = 3 (Pairs of alternate angles)

Substituting 4 and 5 in (1), we get

2 + 1 + 3 = 1800

That is, 1 + 2 + 3 = 1800

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Angle Sum Property Of A Triangle States That The Sum Of All Angles Of A Triangle Is 180 degree

i.e. angle 1+angle2+angle3=180degree

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## Angle Sum Theorem of a Triangle

The sum of the measures of the interior angles of a triangle is 180. • 3 Since angle a, angle b, and angle c make a straight line,

angle a + angle b + angle c = 180 degrees

Since alternate interior angles are equal, angle a = angle x and angle b = angle y

Therefore, angle x + angle y + angle c = 180 degrees

• 4

Angle Sum of a Triangle

With the use of the Parallel Postulate, the following theorem can be proven.

Theorem 25: The sum of the interior angles of any triangle is 180°.

m ∠ A + m ∠ B + m ∠ C = 180°.

Example 1: If m ∠ A = 40° and m ∠ B = 60°, find m ∠ C.

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sum of all the angles of a triange is known as angle sum property

the sum of all angles in a triangle is 180 degree

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