Which of the following is TRUE for every triangle?

Class 7The Triangle and its PropertiesTriangles

AAll three angles are equal.
BThe angles sum to 180°.
CIt has at least one right angle.
DThe longest side is twice the shortest.

Step-by-Step Solution

Only the angle-sum property holds for EVERY triangle. The others are special cases or false.

Answer: B) The angles sum to 180°.

Key idea: Exterior angle property

Extend one side of a triangle past a vertex. The angle formed outside the triangle is the **exterior angle** at that vertex.

**Exterior angle = sum of the two opposite interior angles.**

So if the two non-adjacent interior angles are 50° and 60°, the exterior angle = 50° + 60° = 110°.

Why? The exterior angle and the adjacent interior angle form a linear pair (sum 180°), and the three interior angles also sum to 180°. Subtract: exterior = sum of the other two interior angles.

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