Math Problem Statement

Find m∠JLK.

Solution

The question asks to find the measure of angle JLK\angle JLK. From the image, it looks like we are given a triangle with an angle of 4545^\circ at JKL\angle JKL, and another angle of 9090^\circ at JLK\angle JLK.

To solve this problem:

  1. We know that the sum of the interior angles in any triangle is 180180^\circ.
  2. We are given that JKL=45\angle JKL = 45^\circ.
  3. It seems that JLK=90\angle JLK = 90^\circ based on the right-angle notation.

Therefore, the sum of angles in triangle JKLJKL is: JLK+JKL+KJL=180\angle JLK + \angle JKL + \angle KJL = 180^\circ Substituting the known values: 90+45+KJL=18090^\circ + 45^\circ + \angle KJL = 180^\circ Solving for KJL\angle KJL: KJL=1809045=45\angle KJL = 180^\circ - 90^\circ - 45^\circ = 45^\circ

Thus, the measure of JLK\angle JLK is 9090^\circ, confirming that it's a right triangle.

Would you like more details on this explanation?

Here are 5 related questions for further understanding:

  1. How do you determine the sum of interior angles in a triangle?
  2. What other types of triangles exist based on angle measures?
  3. What is the Pythagorean theorem, and how does it apply to right triangles?
  4. How can you verify if a triangle is a right triangle using angle measures?
  5. Can a triangle have more than one right angle? Why or why not?

Tip: When solving triangle problems, always check for known angle relationships like supplementary, complementary, or right angles to simplify your calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles
Angle Sum Property

Formulas

Sum of angles in a triangle: ∠A + ∠B + ∠C = 180°

Theorems

Triangle Angle Sum Theorem
Right Triangle Properties

Suitable Grade Level

Grades 6-8