https://file.aiquickdraw.com/mathbot/file/17259227160667xr8x42w.jpg

In the image, we have an angle \( \angle HGF \) that is split into two angles, labeled \( (4x - 5)^\circ \) and \( (5x - 15)^\circ \). These two angles are adjacent, and together they form the larger angle \( \angle HGI \), which is a straight line. A straight line measures \( 180^\circ \), so we can set up an equation to find \( x \).

The two angles together must sum to \( 180^\circ \):
\[
(4x - 5) + (5x - 15) = 180
\]

Let's solve for \( x \):

1. Combine like terms:
\[
9x - 20 = 180
\]

2. Add 20 to both sides:
\[
9x = 200
\]

3. Divide both sides by 9:
\[
x = \frac{200}{9} \approx 22.22
\]

So, \( x \approx 22.22 \).

Now, we can substitute this value of \( x \) back into the expressions for the angles:

- \( (4x - 5)^\circ = 4(22.22) - 5 = 88.88 - 5 = 83.88^\circ \)
- \( (5x - 15)^\circ = 5(22.22) - 15 = 111.1 - 15 = 96.1^\circ \)

The two angles are approximately \( 83.88^\circ \) and \( 96.1^\circ \), which indeed sum to \( 180^\circ \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What are adjacent angles, and how are they related?
2. How would you solve a similar problem if the angles formed a triangle instead of a straight line?
3. Can you explain how the sum of angles around a point adds up to 360 degrees?
4. What is the difference between supplementary and complementary angles?
5. How would the problem change if the sum of the two angles were 90 degrees instead of 180 degrees?

**Tip:** Always check that the sum of the calculated angles matches the expected total (e.g., 180° for straight angles or 360° for angles around a point).

In the image, we have an angle ∠HGF split into two angles, (4x - 5)° and (5x - 15)°. These two angles are adjacent and form a straight line, ∠HGI, which is 180°. Solve for x and find the measure of the two angles.

In this problem, we solve for x using the properties of adjacent angles that form a straight line. The angles are given by the expressions (4x - 5)° and (5x - 15)°. Learn how to set up the equation, solve for x, and calculate the measures of the angles.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation