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To solve this problem, we need to understand the concept of supplementary angles. Two angles are considered supplementary if the sum of their measures is \(180^\circ\).

Given:
- \( m\angle 5 = 78^\circ \)
- \( \angle 5 \) is a supplement of \( \angle 6 \)

Since \( \angle 5 \) and \( \angle 6 \) are supplementary, we can write the equation:
\[
m\angle 5 + m\angle 6 = 180^\circ
\]

Plugging in the given value:
\[
78^\circ + m\angle 6 = 180^\circ
\]

Now, solve for \( m\angle 6 \):
\[
m\angle 6 = 180^\circ - 78^\circ = 102^\circ
\]

Therefore, the measure of \( \angle 6 \) is \( 102^\circ \).

Would you like more details or have any other questions?

Here are five related questions for further practice:
1. What is the measure of an angle that is supplementary to a \(45^\circ\) angle?
2. If two angles are supplementary and one measures \(92^\circ\), what is the measure of the other angle?
3. How would the solution change if \( m\angle 5 \) were \(105^\circ\)?
4. What is the difference between supplementary and complementary angles?
5. Can three angles be supplementary? Why or why not?

**Tip:** Remember, supplementary angles always add up to \(180^\circ\), while complementary angles add up to \(90^\circ\).

∠5 is a supplement of ∠6, and m∠5 = 78°. Find m∠6.

Learn how to solve for the measure of angle 6 when given that angle 5 is 78° and the two angles are supplementary. This problem focuses on the geometry concept of supplementary angles, suitable for students in Grades 6-8.

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