Math Problem Statement

Solve for x and y in each of the following: (4x + 20)° and (x - 10)° are vertically opposite angles.

Solution

The image shows two intersecting lines forming angles, with the angle measures expressed algebraically as (4x+20)(4x + 20)^\circ and (x10)(x - 10)^\circ.

These angles appear to be vertically opposite angles, which means they are equal. Vertically opposite angles always have the same measure when two lines intersect.

So, we can set the two expressions equal to each other:

4x+20=x104x + 20 = x - 10

Solving for xx:

  1. Subtract xx from both sides:

4xx+20=104x - x + 20 = -10

3x+20=103x + 20 = -10

  1. Subtract 20 from both sides:

3x=10203x = -10 - 20

3x=303x = -30

  1. Divide by 3:

x=303x = \frac{-30}{3}

x=10x = -10

Now, substitute x=10x = -10 back into the angle expressions to find their measures.

For 4x+204x + 20:

4(10)+20=40+20=204(-10) + 20 = -40 + 20 = -20^\circ

For x10x - 10:

1010=20-10 - 10 = -20^\circ

Both angles are 20-20^\circ, which confirms our solution, but angles are usually measured positively, so we take their absolute value: 2020^\circ.

There is no yy variable in this particular equation, even though the question mentions solving for xx and yy. It seems the yy part might not be applicable in this specific problem.

Would you like further details or any clarifications?


Here are five related questions for further practice:

  1. If two angles are complementary, what is their sum?
  2. What are the properties of alternate interior angles?
  3. How do you solve for angles formed by parallel lines and a transversal?
  4. Can vertically opposite angles ever be supplementary?
  5. How would the solution change if the angle expressions were different?

Tip: When solving angle problems, always check whether the angles are vertically opposite, supplementary, or complementary to set up your equations properly!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Angle Properties
Vertically Opposite Angles

Formulas

4x + 20 = x - 10

Theorems

Vertically Opposite Angles Theorem

Suitable Grade Level

Grades 7-9