知识点 2

Apply triangle angle-sum and related theorems to find unknown angles.

Use the triangle angle sum or the exterior-angle theorem to find unknown angles.

核心知识

The three interior angles of any triangle add up to 180°. An exterior angle of a triangle equals the sum of the two non-adjacent interior angles.

深入理解

Rule: A triangle's angles always add to 180∘.

  • Use the exterior angle theorem when the problem gives an outside angle.
  • If the angles are expressions, set up one equation and solve.
  • Re-read the question so you report the angle it actually asks for.

The algebra is usually simple; the trick is choosing the correct angle relationship.

分步讲解

  1. Label each angle — use the given values or expressions.
  2. Set up the equation: all three interior angles sum to 180°, or use the exterior angle theorem.
  3. Solve for the variable.
  4. Substitute back to find the specific angle the question asks about.

常见误解

  • Forgetting to plug back in — the question usually asks for an angle measure, not just the variable value.
  • Applying the 180° rule to a quadrilateral (which sums to 360°).
  • Confusing an exterior angle with the interior angle next to it.
题目

示例解析

In triangle 𝐴𝐵𝐶, angle 𝐴 measures 42 ° and angle 𝐵 measures 73 °. What is the measure of the exterior angle at vertex 𝐶?

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