Math Problem Statement

Which equation can be used to solve for x, given the angles around point S?

Solution

In the diagram, you have three angles around point SS, which together form a straight line. Since the angles on a straight line add up to 180180^\circ, we can set up an equation using the given angles.

The angles are:

  • QSP=71\angle QSP = 71^\circ
  • RSP=(9x6)\angle RSP = (9x - 6)^\circ
  • RSQ=(2x)\angle RSQ = (2x)^\circ

Equation for a straight line:

71+(9x6)+2x=18071^\circ + (9x - 6)^\circ + 2x^\circ = 180^\circ

Simplify the equation:

71+9x6+2x=18071 + 9x - 6 + 2x = 180 65+11x=18065 + 11x = 180

Solve for xx:

11x=1806511x = 180 - 65 11x=11511x = 115 x=11511x = \frac{115}{11} x10.45x \approx 10.45

Thus, x10.45x \approx 10.45.

Would you like further clarification or a more detailed explanation?

Here are 5 related questions:

  1. How do you derive the equation for angles on a straight line?
  2. What happens if one angle is missing? Can we still solve for xx?
  3. How do supplementary angles relate to this problem?
  4. How do you handle the algebra if xx had been part of multiple terms?
  5. What is the importance of rounding in this type of problem?

Tip: Always check your calculations by adding the angles to ensure they sum to 180180^\circ.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles on a straight line
Algebra

Formulas

Sum of angles on a straight line: 180°
Linear equation manipulation

Theorems

Supplementary angles theorem

Suitable Grade Level

Grades 8-10