Math Problem Statement

What is the measure of the third angle in a right triangle if one angle is 72° and the other is 90°?

Solution

In the image, I see a triangle with one labeled angle of 7272^\circ and an adjacent line with an indicated angle of 9090^\circ, likely suggesting a right angle. This seems to indicate a right triangle with a 90-degree angle, and the 72-degree angle is one of the non-right angles.

To find the remaining angle in the triangle, we use the fact that the sum of angles in a triangle is always 180180^\circ. Therefore, the missing angle, xx, can be calculated as follows:

x=1809072=18x = 180^\circ - 90^\circ - 72^\circ = 18^\circ

Thus, the remaining angle in the triangle is 1818^\circ.

Would you like a more detailed explanation or have any other questions about this?

Here are 5 related questions to think about:

  1. How can you calculate the side lengths of this right triangle if one of the sides is known?
  2. What is the sine, cosine, or tangent of the 72° angle in this triangle?
  3. How would the triangle change if the 72° angle were altered to another value?
  4. Can you identify other types of triangles based on their angle properties (e.g., equilateral or isosceles)?
  5. What are the uses of the Pythagorean theorem in right triangles like this one?

Tip: The sum of interior angles in any triangle always adds up to 180180^\circ, which is helpful for solving many types of triangle-related problems.

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Math Problem Analysis

Mathematical Concepts

Triangle Geometry
Angle Sum Property

Formulas

Sum of angles in a triangle: 180° = 90° + 72° + x

Theorems

Sum of interior angles in a triangle theorem

Suitable Grade Level

Grades 6-8