prove that the sum of the angles of a triangle is 180 degrees
Answers
In order to prove that the sum of angles of a triangle is 180, you must know the theorems of angles of a triangle.
We know that, alternate interior angles are of equal magnitude.
This'll help us get the answer. Let us assume a triangle ABC. Now we have to substitute the angles.
∠PAB + ∠BAC + ∠CAQ = 180°. where PQ line parallel to side BC touching vertex A.
∠PAB = ∠ABC & ∠CAQ = ∠ACB BECAUSE alternate interior angles are congruent..
Hence we get, ∠ABC + ∠BAC + ∠ACB = 180° [Proved]
Solution :-
\sf{\angle 3 + \angle 4 + \angle 5 = 180 \textdegree (Linear\ Pair\ of\ angles) ..(1)}∠3+∠4+∠5=180\textdegree(Linear Pair of angles)..(1)
\sf{ \angle 4 = \angle 1 \ (Alternate\ angles)}∠4=∠1 (Alternate angles)
\sf{ \angle 5 = \angle 2 \ (Alternate\ angles)}∠5=∠2 (Alternate angles)
From eq (1) ;
\sf{\angle 1 + \angle 2 + \angle 3 = 180 \textdegree}∠1+∠2+∠3=180\textdegree
\sf{\angle A + \angle B + \angle C = 180 \textdegree}∠A+∠B+∠C=180\textdegree
Hence, it is proved that sum of angles of a triangle is 180°.
Extra Info About Triangle :-
Triangle has 3 sides. It has 3 angles. The sum of angles of triangle is always be 180°. There are 3 types of triangle :-
• Equilateral Triangle (All sides are equal)
• Isosceles Triangle (Two of three sides are equal)
• Scalene Triangle (No side is equal)