Math Problem Statement

Find the value of the missing angle in a right triangle where one angle is 64°.

Solution

This image shows a right triangle with a given angle of 64° and another angle labeled xx^\circ. Since the sum of the interior angles of any triangle is always 180°, we can use that fact to determine the value of xx.

In a right triangle, one of the angles is always 90°, so:

x+64+90=180x + 64^\circ + 90^\circ = 180^\circ

Simplifying:

x+154=180x + 154^\circ = 180^\circ

Solving for xx:

x=180154=26x = 180^\circ - 154^\circ = 26^\circ

So, the value of xx is 2626^\circ.

Let me know if you would like any further details or explanations! Here are some related questions to think about:

  1. How would the calculation change if one of the other angles was unknown instead of xx?
  2. Can you explain why the sum of the angles in a triangle always equals 180°?
  3. What would be the sum of the angles if this were not a right triangle?
  4. How does the Pythagorean theorem apply to right triangles like this one?
  5. How can you classify this triangle based on its angles?

Tip: Always remember that in any triangle, the sum of all interior angles is 180°, which is especially useful when solving for unknown angles.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles
Angle Sum in Triangles

Formulas

Sum of angles in a triangle: 180°
Right angle: 90°

Theorems

Angle Sum Theorem

Suitable Grade Level

Grades 6-8