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What is the sum of all …

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What is the sum of all angles of a triangle?

Posted by Abhay Pratap Singh 4 years, 1 month ago

CBSE > Class 05 > Mathematics

4 answers

Amrit Raj 4 years, 1 month ago

180 degrees

Mehal Khunti 4 years, 1 month ago

180

Gaurav Seth 4 years, 1 month ago

180

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Proof:

Consider a ∆ABC, as shown in the figure below. To prove the above property of triangles, draw a line PQ←→ parallel to the side BC of the given triangle.

Since PQ is a straight line, it can be concluded that:

∠PAB + ∠BAC + ∠QAC = 180° ………(1)

Since PQ||BC and AB, AC are transversals,

Therefore, ∠QAC = ∠ACB (a pair of alternate angle)

Also, ∠PAB = ∠CBA (a pair of alternate angle)

Substituting the value of ∠QAC and∠PAB in equation (1),

∠ACB + ∠BAC + ∠CBA= 180°

Thus, the sum of the interior angles of a triangle is 180°.

Yogita Ingle 4 years, 1 month ago

The sum of all angles of a triangle is 180 degree.

ANSWER

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