Math Problem Statement

What is the equation you would use to find x?

Solution

The question asks to find the correct equation to determine xx in the triangle RST\triangle RST. Here’s the reasoning based on the diagram:

  1. Understanding the Triangle: The triangle is isosceles, meaning two sides are equal, and thus the two base angles at RR and SS are also equal.

  2. Angle Notation:

    • T=3x\angle T = 3x degrees
    • Both R\angle R and S\angle S are each xx degrees, because they are base angles in an isosceles triangle.
  3. Triangle Sum Property: The sum of the interior angles of a triangle is always 180180^\circ. Therefore, we can set up the equation: 3x+x+x=1803x + x + x = 180 Simplifying this, we get: 5x=1805x = 180

  4. Answer Choice: The correct answer is: 3x+x+x=1803x + x + x = 180

Let me know if you need further details or explanation!


Here are five related questions for practice:

  1. How would you solve for xx after setting up the equation 5x=1805x = 180?
  2. What if one of the angles in an isosceles triangle was known; how would you find the other angles?
  3. What is the general property of the sum of angles in any polygon, not just a triangle?
  4. How would the equation change if T=4x\angle T = 4x instead of 3x3x?
  5. What distinguishes an isosceles triangle from an equilateral triangle?

Tip: For any triangle, always remember that the sum of its interior angles is 180180^\circ.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Triangle Sum Property

Formulas

3x + x + x = 180

Theorems

Triangle Sum Theorem

Suitable Grade Level

Grade 8-10