https://file.aiquickdraw.com/mathbot/file/17261691212540pmvwiy4.jpg

We are given that ∠EFG is a right angle, which means that its measure is 90°. The angles ∠EFH and ∠HFG are labeled as expressions in terms of \(x\):

- \( m\angle EFH = 2x + 2 \)
- \( m\angle HFG = (x + 1) \)

Since the sum of angles in a straight line at a point (∠EFH + ∠HFG) must equal 90°, we can set up the following equation:

\[
(2x + 2) + (x + 1) = 90
\]

Let's solve for \(x\):

\[
2x + 2 + x + 1 = 90
\]
\[
3x + 3 = 90
\]
\[
3x = 87
\]
\[
x = 29
\]

Now that we know \(x = 29\), we can find the measures of the two angles:

1. \( m\angle EFH = 2x + 2 = 2(29) + 2 = 58 + 2 = 60^\circ \)
2. \( m\angle HFG = (x + 1) = 29 + 1 = 30^\circ \)

Thus, the measures are:
- \( m\angle EFH = 60^\circ \)
- \( m\angle HFG = 30^\circ \)

Would you like further details on this solution or have additional questions?

### Related Questions:
1. What is the sum of angles around a point on a straight line?
2. How do we determine if two angles are supplementary or complementary?
3. Can you find the value of \(x\) if the total angle is a straight line (180°)?
4. How does the angle sum property apply to triangles?
5. What is the process for solving equations with two or more unknowns?

**Tip:** Always check the sum of angles in a geometric figure to ensure your solution fits the given conditions.

Given that ∠EFG is a right angle, find m∠EFH and m∠HFG. The angles are expressed as (2x + 2)° and (x + 1)°, respectively.

Learn how to find the measures of angles m∠EFH and m∠HFG given algebraic expressions and the fact that ∠EFG is a right angle. This problem covers geometric concepts and basic algebraic solving techniques, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation