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In this problem, we are told that angles \( \angle E \) and \( \angle F \) are supplementary. This means that their measures must add up to \( 180^\circ \).

We are also given the following expressions for these angles:
- \( \angle E = 7x + 16 \)
- \( \angle F = 8x + 14 \)

Since supplementary angles sum to 180°, we can set up the equation:
\[
\angle E + \angle F = 180
\]
Substituting the given expressions for \( \angle E \) and \( \angle F \):
\[
(7x + 16) + (8x + 14) = 180
\]

Now, let's simplify and solve for \( x \):
\[
7x + 8x + 16 + 14 = 180
\]
\[
15x + 30 = 180
\]
Subtract 30 from both sides:
\[
15x = 150
\]
Now divide both sides by 15:
\[
x = 10
\]

### Now that we know \( x = 10 \), we can find the measures of \( \angle E \) and \( \angle F \).

1. \( \angle E = 7x + 16 = 7(10) + 16 = 70 + 16 = 86^\circ \)
2. \( \angle F = 8x + 14 = 8(10) + 14 = 80 + 14 = 94^\circ \)

So:
- \( x = 10 \)
- \( \angle E = 86^\circ \)
- \( \angle F = 94^\circ \)

Would you like any further details or clarification?

### Related questions:
1. What are complementary angles, and how do they differ from supplementary angles?
2. If the angles were complementary instead of supplementary, how would you set up the equation?
3. How can we check if the sum of two angles makes them supplementary?
4. Can supplementary angles be obtuse or acute?
5. How does the relationship between angles help in geometry proofs?

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

∠E and ∠F are supplementary. If ∠E = 7x + 16 and ∠F = 8x + 14 then solve for x and find the measurement of ∠E and ∠F.

Learn how to solve for x in the equation involving supplementary angles ∠E and ∠F, where ∠E = 7x + 16 and ∠F = 8x + 14. Understand how to use algebra and the supplementary angles theorem to find x and the individual angle measures. This problem is suitable for students in Grades 8-10.

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