Math Problem Statement

Solve for x in the equation where the angles are supplementary: 13x - 3 + 75 = 180.

Solution

The image you uploaded appears to be a geometry problem where you're asked to solve for xx in the equation involving angles and lines.

The diagram shows two lines intersecting, forming angles. The equation given is 13x313x - 3, and the angle shown is 7575^\circ.

To solve for xx, you need to use the fact that the angles on a straight line sum up to 180180^\circ.

Here’s how we can approach it:

  1. The given angle is 7575^\circ.
  2. The expression 13x313x - 3 represents the other angle formed by the lines.
  3. These two angles are supplementary, meaning they add up to 180180^\circ.

So, the equation we can set up is:

13x3+75=18013x - 3 + 75 = 180

Now, solve for xx:

  1. Combine like terms:

13x3+75=180    13x+72=18013x - 3 + 75 = 180 \implies 13x + 72 = 180

  1. Subtract 72 from both sides:

13x=18072    13x=10813x = 180 - 72 \implies 13x = 108

  1. Divide both sides by 13:

x=108138.31x = \frac{108}{13} \approx 8.31

However, this result doesn't match any of the given options in the multiple choice. Could you check if the options or values are correctly displayed, or perhaps if there's another part of the equation I missed?

Would you like further clarification on this?

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Linear Equations

Formulas

Sum of supplementary angles = 180°
Solving linear equations

Theorems

Supplementary Angles Theorem

Suitable Grade Level

Grades 8-10