Question

Angle sum property : to verify that the sum of all interior angles of a triangle is 180°

Answer 1

Answer:

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

Consider a ∆ABC, as shown in the figure below. To prove the above property of triangles, draw a line  

←→

P

Q

parallel to the side BC of the given triangle.

Angle sum property of a triangle theorem 1

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°.

Answer 2

Answer:

The angle sum property of a triangle says that the sum of its interior angles is equal to 180°. Whether a triangle is an acute, obtuse, or a right triangle, the sum of the angles will always be 180°. This can be represented as follows: In a triangle ABC, ∠A + ∠B + ∠C = 180°.

Hope it was helpful!!