Math Problem Statement

In the figure, m∠1 = (x−12)° and m∠2 = (5x)°. (a) Write an equation to find x. (b) Find the degree measure of each angle.

Solution

To solve the problem, let's break it down step by step:

Given:

  1. m1=(x12)m\angle 1 = (x - 12)^\circ
  2. m2=(5x)m\angle 2 = (5x)^\circ

Observations:

  • 1\angle 1 and 2\angle 2 are adjacent angles forming a straight line.
  • The sum of the angles on a straight line is 180180^\circ.

(a) Write an equation to find xx:

The equation can be written as:

m1+m2=180m\angle 1 + m\angle 2 = 180^\circ

Substitute the given expressions for m1m\angle 1 and m2m\angle 2:

(x12)+(5x)=180(x - 12) + (5x) = 180

Simplify the equation:

6x12=1806x - 12 = 180

Add 12 to both sides:

6x=1926x = 192

Divide both sides by 6:

x=32x = 32


(b) Find the degree measure of each angle:

Now that x=32x = 32, substitute xx into the expressions for m1m\angle 1 and m2m\angle 2.

  1. m1=x12m\angle 1 = x - 12: m1=3212=20m\angle 1 = 32 - 12 = 20^\circ

  2. m2=5xm\angle 2 = 5x: m2=5(32)=160m\angle 2 = 5(32) = 160^\circ


Final Answers:

  1. Equation: (x12)+5x=180(x - 12) + 5x = 180
  2. Degree Measures:
    • m1=20m\angle 1 = 20^\circ
    • m2=160m\angle 2 = 160^\circ

Let me know if you need any clarifications!


Related Questions:

  1. What is the sum of adjacent angles on a straight line?
  2. How would you solve for xx if 1\angle 1 and 2\angle 2 were vertical angles?
  3. What is the general formula for angles that form a linear pair?
  4. If m2=3xm\angle 2 = 3x instead, how would the solution change?
  5. How can you check if your solutions for m1m\angle 1 and m2m\angle 2 are correct?

Tip:

Always check your final answers by verifying that the sum of the angles equals 180180^\circ.

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Math Problem Analysis

Mathematical Concepts

Linear Pairs
Angle Relationships
Basic Algebra

Formulas

Sum of angles on a straight line = 180°

Theorems

Linear Pair Theorem

Suitable Grade Level

Grades 6-8