Angle F and angle G are complementary. Angle F measures (2x+7) degrees and angle G measures 18 degrees. Find the Value of X and the Measure of each angle.

We are told that angles F and G are complementary, which means their sum is 90°:

\[
\text{Angle F} + \text{Angle G} = 90°
\]

You are given:
- Angle F = \(2x + 7^\circ\)
- Angle G = \(18^\circ\)

Now, we can set up the equation:

\[
(2x + 7) + 18 = 90
\]

Simplify this:

\[
2x + 25 = 90
\]

Subtract 25 from both sides:

\[
2x = 90 - 25
\]
\[
2x = 65
\]

Now, divide both sides by 2 to solve for \(x\):

\[
x = \frac{65}{2}
\]
\[
x = 32.5
\]

Now that we know \(x = 32.5\), we can find the measure of each angle:

- Angle F = \(2x + 7 = 2(32.5) + 7 = 65 + 7 = 72^\circ\)
- Angle G = \(18^\circ\) (already given)

Thus, the value of \(x\) is 32.5, and:
- Angle F measures \(72^\circ\)
- Angle G measures \(18^\circ\)

Would you like a more detailed breakdown or any clarification on the steps?

Here are 5 related questions to explore further:
1. How do complementary angles differ from supplementary angles?
2. What is the relationship between angles in a triangle?
3. How do you solve for \(x\) when angles are supplementary?
4. Can complementary angles be non-adjacent, or must they be next to each other?
5. How do you solve for unknown angles using algebra in geometry?

**Tip:** Always remember that complementary angles add up to 90°, while supplementary angles add up to 180°.

Learn how to solve for the unknown value of X in complementary angles where Angle F is (2x+7) degrees and Angle G is 18 degrees. This solution involves basic algebraic steps and the Complementary Angles Theorem. Suitable for students in Grades 6-8.

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