To solve this problem, we know that two angles are complementary if their sum equals 90 degrees.

Step 1: Set up the equation for complementary angles

Given:

• Angle F measures $(2x + 7)^\circ$
• Angle G measures $18^\circ$

Since the angles are complementary, their sum is 90 degrees: $(2x + 7) + 18 = 90$

Step 2: Solve for $x$

Now, simplify the equation: $2x + 25 = 90$ Subtract 25 from both sides: $2x = 90 - 25$ $2x = 65$ Now, divide both sides by 2: $x = \frac{65}{2} = 32.5$

Step 3: Find the measure of each angle

Now that we have $x = 32.5$, substitute this value into the expression for angle F: $\text{Angle F} = 2(32.5) + 7 = 65 + 7 = 72^\circ$ So, angle F measures $72^\circ$.

For angle G, we already know it is $18^\circ$.

Final Answer:

• $x = 32.5$
• Measure of angle F = $72^\circ$
• Measure of angle G = $18^\circ$

Let me know if you'd like more details or have any other questions!

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Here are 5 related questions to explore:

1. What happens if the angles were supplementary instead of complementary?
2. How do you solve for unknown angles in a triangle?
3. What is the difference between complementary and supplementary angles?
4. How can you use algebra to solve for unknown angles in polygons?
5. What would the angles be if angle F measured $(3x + 5)^\circ$ instead?

Tip: When solving for an unknown variable in angle problems, always pay attention to the type of angle relationship (complementary, supplementary, etc.), as it gives you the equation you need!