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In a triangle, can two angles each measure 95°?

Class 9Triangles (Congruence)Geometry — Triangles
  • ANo, because two 95° angles already add up to more than 180°
  • BYes, if the third angle is very small
  • CYes, in an obtuse-angled triangle
  • DNo, because a triangle cannot have any angle above 90°

Step-by-Step Solution

Two angles of 95° each sum to 190°, already more than 180°, which is impossible since all three angles must sum to exactly 180°.
Answer: A) No, because two 95° angles already add up to more than 180°

Key idea: Inequalities in a triangle

**Property 1**: In a triangle, the side opposite the LARGER angle is LONGER. (Bigger angle stretches the opposite side.)

**Property 2**: Conversely, the angle opposite the longer side is larger.

**Property 3 (Triangle Inequality)**: The sum of any two sides of a triangle is GREATER than the third side.

This means three given lengths form a triangle ONLY IF each pair sums to more than the third.

Example: Can 2, 3, 6 form a triangle? Check: 2 + 3 = 5 < 6. NO.

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