Math Problem Statement

The measures of the angles of a triangle are shown in the figure below. Solve for x.

Solution

To solve for xx^\circ in this triangle, we can use the angle sum property of triangles, which states that the sum of the angles in any triangle is always 180180^\circ.

In the given triangle:

  • One angle is 4444^\circ,
  • Another angle is a right angle, which is 9090^\circ,
  • The third angle is xx^\circ, which we need to find.

Using the formula for the sum of the angles in a triangle:

x+90+44=180x^\circ + 90^\circ + 44^\circ = 180^\circ

Now, simplify this equation:

x+134=180x^\circ + 134^\circ = 180^\circ

Solve for xx:

x=180134=46x^\circ = 180^\circ - 134^\circ = 46^\circ

Thus, the value of xx is 4646^\circ.

Would you like more details, or do you have any questions?

Here are five related questions:

  1. What is the sum of the angles in a quadrilateral?
  2. How can the Pythagorean theorem be applied to right triangles?
  3. What are the properties of an isosceles triangle?
  4. How do you find the exterior angles of a triangle?
  5. Can a triangle have more than one right angle?

Tip: Always check if the triangle has a right angle, as it simplifies calculations significantly.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angle Sum Property
Triangles

Formulas

Sum of angles in a triangle: x + 90° + 44° = 180°

Theorems

Angle Sum Theorem

Suitable Grade Level

Grades 6-8