Suppose there is a Triangle which have sides AB , BC and CD

Draw a line PQ passes through point A such that PQ is parallel to BC .

Before proving this theorem, you should know about that alternate int angles are equal and about the linear Pair .

Now you can simply do this .

Try yourself.

This is only a hint

Understanding the Triangle Angle Sum
The sum of the angles in a triangle is always 180 degrees. This can be proven using a simple geometric construction.

Step 1: Draw a Triangle
- Start by drawing triangle ABC, with angles A, B, and C.

Step 2: Extend a Base
- Extend the base BC to the right, creating a line.

Step 3: Draw a Parallel Line
- Through point A, draw a line parallel to BC. This will intersect the extended line at point D.

Step 4: Identify Corresponding Angles
- The angle A (∠CAB) and the angle formed at D (∠DAB) are alternate interior angles, hence they are equal.
- Similarly, angle B (∠ABC) and angle C (∠ACD) are also corresponding angles. Thus, ∠ABC = ∠ACD.

Step 5: Sum the Angles
- Now, look at the straight line formed by points D, B, and C. The angle sum around point A on the straight line gives us:
- ∠DAB + ∠ABC + ∠ACD = 180 degrees
- Substituting the equal angles:
- ∠A + ∠B + ∠C = 180 degrees

Conclusion
This geometric proof shows that the sum of the angles in any triangle will always equal 180 degrees. This fundamental property is essential in various applications of geometry and trigonometry.