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Let's solve this step-by-step.

### Given Information:
- \( m \angle P \) is three less than twice the measure of \( m \angle Q \).
- \( \angle P \) and \( \angle Q \) are supplementary angles.

### Definitions and Equations:
1. **Supplementary Angles** means their sum is 180°:
   \[
   m \angle P + m \angle Q = 180^\circ
   \]

2. Let the measure of \( \angle Q \) be \( x \). Then, the measure of \( \angle P \) is three less than twice \( x \):
   \[
   m \angle P = 2x - 3
   \]

### Set up the equation:
Using the fact that the two angles are supplementary:
\[
(2x - 3) + x = 180
\]

### Solve for \( x \):
1. Combine like terms:
   \[
   3x - 3 = 180
   \]
   
2. Add 3 to both sides:
   \[
   3x = 183
   \]

3. Divide by 3:
   \[
   x = 61
   \]

### Find the measures of both angles:
- \( m \angle Q = x = 61^\circ \)
- \( m \angle P = 2x - 3 = 2(61) - 3 = 122 - 3 = 119^\circ \)

### Final Answer:
- \( m \angle P = 119^\circ \)
- \( m \angle Q = 61^\circ \)

Would you like further details on this? Here are five questions to expand on this topic:

1. What are complementary angles and how are they different from supplementary angles?
2. How do we set up equations when angles are expressed in terms of variables?
3. What are some real-life applications of supplementary angles?
4. Can two obtuse angles be supplementary?
5. How do we solve angle problems when both angles are expressed with unknowns?

**Tip:** Always remember, supplementary angles sum up to 180°, and complementary angles sum up to 90°.

If m∠P is three less than twice the measure of ∠Q, and ∠P and ∠Q are supplementary angles, find each angle measure.

Learn how to solve a supplementary angles problem where m∠P is three less than twice m∠Q. Follow the step-by-step guide using algebra and geometry concepts. Suitable for students in Grades 7-10.

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