Question

prove thet the sum of three angles of a triangle is 180 ​

Answer 1

THREOM

The angle sum property of a triangle states that the angles of a triangle always add up to 180°.[6] Every triangle has three angles and whether it is an acute, obtuse, or right triangle, the som of angles 180°.

For example, in triangle ABC, angle A + angle B + angle C = 180°.

EXAMPLES ARE:-

To really grasp this concept, it can be helpful to study some examples. Look at the right triangle, where one of the angles is 90°, and the other angles each measure 45°. Summing 90° + 45° + 45° = 180°. Study other triangles of various shapes and sizes and sum their angles. You will see that they always add up to 180°.[7]

For the right triangle example: angle A = 90°, angle B = 45°, and angle C = 45°. The theorem states that angle A + angle B + angle C = 180°. Adding the angles gives you 90° + 45° + 45° = 180°. Therefore, the left-hand side (L.H.S.) equals the right-hand side (R.H.S.).

PROVED BY THREOM IS:-

Using simple algebra, you can use the angle sum theorem to solve for an unknown angle if you know the other two angles of the triangle. Rearrange the basic equation to solve for the unknown angle.

For example, in triangle, ABC, angle A = 67° and angle B = 43°, but angle C is unknown.

angle A + angle B + angle C = 180°

67° + 43° + angle C = 180°

angle C = 180° - 67° - 43°

angle C = 70°

OR IN VERY SIMPLE WAY IS:-

SUM OF THREE ANGLES OF TRIANGLE IS 180

SO LET TAKE THREE ANGLES AS X SO, 3X

⇒3X = 180

⇒ X = 180/3

⇒ X = 60