There are two parts to this question.

Question

PART A:

Angles FEG and DEG are complementary angles. The equation to solve for x is: (5x−22)°+(2x)°=90°.

Fill in the blanks with the correct steps for solving for x.

(3 points)
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Steps to solve for x:

5x−22+2x=90 Original Equation
7x−22=90 Response area
7x=112 Response area
x=16 Response area


Question 2
PART B:

Determine the measure of each angle using the solution x = 16.

(2 points)
The m ∠ FEG =
degrees

The m ∠ DEG =
degrees

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Answer 1

Let's complete Part A first by filling in the blanks with the correct steps for solving for \( x \).

Part A:

1. Original Equation:
   \( (5x−22)° + (2x)° = 90° \)

2. Combine Like Terms:
   \( 5x−22 + 2x = 90 \)
   This simplifies to:
   \( 7x−22 = 90 \)

3. Add 22 to Both Sides:
   \( 7x−22 + 22 = 90 + 22 \)
   This simplifies to:
   \( 7x = 112 \)

4. Divide by 7:
   \( x = \frac{112}{7} \)
   This simplifies to:
   \( x = 16 \)

So, the completed steps for Part A are:

• \( 7x−22 = 90 \)
• \( 7x = 112 \)
• \( x = 16 \)

Part B:

Now, let's determine the measure of each angle using the solution \( x = 16 \).

1. Measure of angle FEG:
   \( m ∠FEG = (5x - 22)° \)
   Substituting \( x = 16 \):
   \( m ∠FEG = 5(16) - 22 = 80 - 22 = 58° \)

2. Measure of angle DEG:
   \( m ∠DEG = (2x)° \)
   Substituting \( x = 16 \):
   \( m ∠DEG = 2(16) = 32° \)

Thus, the answers for Part B are:

• The measure of \( m ∠FEG = 58° \)
• The measure of \( m ∠DEG = 32° \)

Please fill in the final values as follows:

• The m ∠ FEG = 58 degrees
• The m ∠ DEG = 32 degrees