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In triangle XYZ, XY = XZ and angle X = 104°. Which side is the longest?

Class 7The Triangle and its PropertiesTriangles
  • AXY
  • BYZ
  • CXZ
  • DAll three sides are equal

Step-by-Step Solution

Since XY = XZ, the base angles are equal: angle Y = angle Z = (180 − 104) ÷ 2 = 38°. The largest angle is angle X = 104°, and the longest side lies opposite the largest angle. The side opposite X is YZ. Trap: choosing XY or XZ because they are the two named equal sides — being equal to each other does not make them the longest.
Answer: B) YZ

Key idea: Side-angle relationship

**The longest side of a triangle is opposite the largest angle. The shortest side is opposite the smallest angle.**

In an isosceles triangle, the two equal sides face equal angles. In an equilateral triangle, all sides equal → all angles 60°.

This lets you order sides if you know the angles, or vice versa, even without computing exact values.

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