https://file.aiquickdraw.com/mathbot/file/1726539174987jz1on2sr.jpg

We are given two angles:

- \( m\angle 1 = (x - 9)^\circ \)
- \( m\angle 2 = 6x^\circ \)

From the figure, it appears that these two angles are supplementary because they form a straight line. Therefore, their sum should be 180°:

\[
m\angle 1 + m\angle 2 = 180^\circ
\]

Substituting the expressions for the angles:

\[
(x - 9) + 6x = 180
\]

Now, let's solve for \(x\):

\[
x - 9 + 6x = 180
\]
\[
7x - 9 = 180
\]
\[
7x = 180 + 9
\]
\[
7x = 189
\]
\[
x = \frac{189}{7}
\]
\[
x = 27
\]

Now that we have the value of \(x\), we can substitute it back into the expressions for \(m\angle 1\) and \(m\angle 2\).

\[
m\angle 1 = (x - 9) = 27 - 9 = 18^\circ
\]
\[
m\angle 2 = 6x = 6 \times 27 = 162^\circ
\]

Thus, the angle measures are:
- \( m\angle 1 = 18^\circ \)
- \( m\angle 2 = 162^\circ \)

Would you like more details or have any questions?

Here are five related questions:
1. What are supplementary angles?
2. How do you determine if angles are supplementary or complementary?
3. How do you solve for \(x\) in a linear equation?
4. Can two acute angles be supplementary?
5. What are some other types of angle relationships?

**Tip:** When solving equations involving angles, always verify whether the angles are supplementary, complementary, or congruent to set up the correct equation.

In the figure below, m∠1 = (x - 9)° and m∠2 = 6x°. Find the angle measures.

Learn how to solve a geometry problem where two angles, expressed as m∠1 = (x - 9)° and m∠2 = 6x°, form a straight line. The solution includes step-by-step calculations and algebraic techniques. Suitable for Grades 7-9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation