Math Problem Statement

Find the value of x in a right triangle where one angle is 59°, and the unknown angle is x.

Solution

Let's analyze the problem from the image.

We are given a right triangle with two angles:

  • One angle is 5959^\circ.
  • The other non-right angle is labeled xx^\circ.

Since this is a right triangle, the sum of all angles must be 180180^\circ. One of the angles is a right angle (which is 9090^\circ). Hence, we can set up the equation for the sum of the angles:

x+59+90=180x + 59^\circ + 90^\circ = 180^\circ

Solving for xx:

x+149=180x + 149^\circ = 180^\circ x=180149x = 180^\circ - 149^\circ x=31x = 31^\circ

Final Answer:

x=31x = 31^\circ

Let me know if you have any questions or need further clarifications!


Related Questions:

  1. How do you find the unknown angle in a right triangle?
  2. Why do the angles of any triangle always sum to 180180^\circ?
  3. What are complementary angles, and how are they relevant to right triangles?
  4. How do trigonometric functions like sine or cosine relate to the angles in right triangles?
  5. What is the difference between an acute, obtuse, and right angle?

Tip: Always double-check the known and unknown values when setting up your equations to avoid small arithmetic mistakes.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles in a Triangle

Formulas

Sum of angles in a triangle = 180°

Theorems

Angle sum property of a triangle

Suitable Grade Level

Grades 6-8