Question

Q19. State and prove Angle sum property of a triangle. Using this result, find the value of p and all the
three angles of a triangle , if the angles are (3x-2), (2x +11)' and (5x-9).​

Answer 1

Angle Sum Property of a Triangle Theorem :

In the given triangle, ∆ABC, AB, BC, and CA represent three sides. A, B and C are the three vertices and ∠ABC, ∠BCA and ∠CAB are three interior angles of ∆ABC.

Angle Sum Property of a Triangle

Theorem 1: 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.

Proof for Angle Sum Property of a Triangle

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

∠PAB + ∠BAC + ∠QAC = 180° ………(1)

SincePQ||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:

180=180

Step-by-step explanation:

3x-2+2x+11+5x-9=180

10x=180

x=180/10

x=18

3x-2

3*18-2

52.

2x+11

2*18+11

47.

5x-9

5*18-9

81.

52+47+81=180

angle sum property =180

Therefore proved.