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A triangle is possible only if:

• The angle is less than 180°
If angle ≥ 180°, triangle cannot be formed.

Case 2: Two Angles and the Included Side

Concept
When two angles and the side between them are given, the triangle can be constructed by
forming both angles.
Construction Steps (Example)
Given: AB = 5 cm, ∠A = 45°, ∠B = 80°
1. Draw base AB = 5 cm
2. Construct ∠A = 45° at A
3. Construct ∠B = 80° at B
4. The two arms intersect at point C

ΔABC is formed

Diagram 2: Two Angles and Included Side

Construction using two angles and the included side (ASA method)

Do Triangles Always Exist in This Case?
Not always.
A triangle exists only when:

Sum of two given angles < 180°
If:
• Sum = 180° → Lines form a straight line
• Sum > 180° → Lines do not meet

Finding the Third Angle

If two angles are known, the third angle can be determined.

The sum of all three angles of a triangle is always 180°

Example:
• ∠B = 50°, ∠C = 70°