https://file.aiquickdraw.com/mathbot/file/1726144912891d2ntxd1e.jpg

The problem in the image is asking to solve for \( m \angle GHI \) given that:

\[
m \angle GHJ = 96^\circ \quad \text{and} \quad m \angle JHI = 66^\circ
\]

From the diagram, we can observe that:

- \( \angle GHJ \) and \( \angle JHI \) form a straight line, meaning their measures add up to \( 180^\circ \).
- \( m \angle GHI \) is the angle we are solving for.

Using the relationship that:

\[
m \angle GHJ + m \angle GHI + m \angle JHI = 180^\circ
\]

Substitute the given values:

\[
96^\circ + m \angle GHI + 66^\circ = 180^\circ
\]

Simplify:

\[
162^\circ + m \angle GHI = 180^\circ
\]

Now solve for \( m \angle GHI \):

\[
m \angle GHI = 180^\circ - 162^\circ = 18^\circ
\]

Thus, the measure of \( m \angle GHI \) is \( 18^\circ \).

Would you like further details on this solution? Here are some related questions for practice:

1. How do we know that the angles on a straight line add up to 180°?
2. What is the relationship between adjacent angles formed by a straight line?
3. Can you explain what a supplementary angle is?
4. How do you solve for an unknown angle when given two other angles on a straight line?
5. How would the solution change if one of the angles was unknown?

**Tip:** Always verify whether the angles form a straight line to use the property that their sum is 180°.

Solve for m∠GHI if m∠GHJ = 96° and m∠JHI = 66°.

Learn how to solve for angle GHI when given that angles GHJ and JHI form a linear pair. The solution uses the property that the sum of angles on a straight line is 180°. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation