In the earlier classes- you have tudied through activities that the sum of all tha angles of a tiangle is 180 - We can prove this statement using the axioms and theorems related to parallel lines-

Draw XY parallel to QR #10; #10; XY∥ QR #10; #10; ∠ 2 = ∠ 4 (transversal) #8230; #8230; #8230; #8230; #10;(1) #10; #10; ∠ ...

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Standard VII

Mathematics

Angle Sum Property

In the earlie...

Question

In the earlier classes, you have tudied through activities that the sum of all tha angles of a tiangle is $180^{\circ}$ . We can prove this statement using the axioms and theorems related to parallel lines.

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Solution

Draw XY parallel to QR

$X Y ∥ Q R$

$∠ 2 = ∠ 4$ (transversal) ………… (1)

$∠ 3 = ∠ 5$ (transversal )…………….(2)

Also $∠ 1 + ∠ 4 + ∠ 5 = 180$

$∠ 1 + ∠ 2 + ∠ 3 = 180$ by (1) and (2)

Hence sum of all angle of triangle is 180

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In the earlier classes, you have tudied through activities that the sum of all tha angles of a tiangle is 180∘. We can prove this statement using the axioms and theorems related to parallel lines.

Draw XY parallel to QR XY∥QR ∠2=∠4 (transversal) ………… (1) ∠3=∠5 (transversal )…………….(2) Also ∠1+∠4+∠5=180 ∠1+∠2+∠3=180 by (1) and (2) Hence sum of all angle of triangle is 180

In the earlier classes, you have tudied through activities that the sum of all tha angles of a tiangle is $180^{\circ}$ . We can prove this statement using the axioms and theorems related to parallel lines.

Draw XY parallel to QR

$X Y ∥ Q R$

$∠ 2 = ∠ 4$ (transversal) ………… (1)

$∠ 3 = ∠ 5$ (transversal )…………….(2)

Also $∠ 1 + ∠ 4 + ∠ 5 = 180$

$∠ 1 + ∠ 2 + ∠ 3 = 180$ by (1) and (2)

Hence sum of all angle of triangle is 180