Math Problem Statement

Find the measure of each angle indicated in the triangle, where ∠TUN = 134° and ∠STU = 114°. Solve for ∠TUS.

Solution

Let’s analyze the question in the uploaded image.

We are solving for the measure of angle TUS\angle TUS in the given triangle. Here’s how we solve it step by step:

  1. Identify Given Angles:

    • TUN=134\angle TUN = 134^\circ (on the left).
    • STU=114\angle STU = 114^\circ (on the top).
  2. Sum of Angles in a Triangle: The sum of the interior angles of any triangle is always 180180^\circ. Therefore: TUN+STU+TUS=180\angle TUN + \angle STU + \angle TUS = 180^\circ

  3. Substitute Known Values: Substitute the given angles: 134+114+TUS=180134^\circ + 114^\circ + \angle TUS = 180^\circ

  4. Solve for TUS\angle TUS: Simplify: 248+TUS=180248^\circ + \angle TUS = 180^\circ Subtract 248248^\circ from both sides: TUS=180248\angle TUS = 180^\circ - 248^\circ TUS=68\angle TUS = -68^\circ


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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Angles
Angle Sum Property

Formulas

Sum of angles in a triangle = 180°

Theorems

Triangle Angle Sum Theorem

Suitable Grade Level

Grades 6-8