Toni is analyzing two adjacent angles named MM and RR. The sum of the angles is 180°180° where the measure of ∠M∠M is (4x + 20)∘(4x + 20)∘ and the measure of ∠R∠R is 36∘36∘.

To solve this, let's set up an equation based on the information given:

1. **Given Information**:  
   - \( \angle M + \angle R = 180^\circ \)
   - \( \angle M = (4x + 20)^\circ \)
   - \( \angle R = 36^\circ \)

2. **Set Up Equation**:  
   Substitute the values of \( \angle M \) and \( \angle R \) into the equation for the sum of the angles:
   \[
   (4x + 20) + 36 = 180
   \]

3. **Solve for \( x \)**:
   \[
   4x + 20 + 36 = 180
   \]
   Simplify:
   \[
   4x + 56 = 180
   \]
   Subtract 56 from both sides:
   \[
   4x = 124
   \]
   Divide by 4:
   \[
   x = 31
   \]

4. **Find \( \angle M \)**:
   Substitute \( x = 31 \) back into \( \angle M = (4x + 20) \):
   \[
   \angle M = 4(31) + 20 = 124 + 20 = 144^\circ
   \]

5. **Verify**:
   \[
   \angle M + \angle R = 144^\circ + 36^\circ = 180^\circ
   \]

**Solution**: \( x = 31 \), and the measure of \( \angle M \) is \( 144^\circ \).

Would you like a further breakdown, or do you have questions about any of these steps?

---

1. If \( x = 31 \), what would be the measure of an angle adjacent to \( \angle M \) in a different scenario?
2. How would the equation change if \( \angle R \) were \( (5x + 10)^\circ \) instead of \( 36^\circ \)?
3. What is the general rule for finding the measure of angles that add up to \( 180^\circ \)?
4. Could you find \( x \) if the sum of \( \angle M \) and \( \angle R \) was not \( 180^\circ \), but rather \( 150^\circ \)?
5. How can you verify whether two angles are supplementary?

**Tip**: In geometry, angles that add up to \( 180^\circ \) are known as supplementary angles.

Toni is analyzing two adjacent angles named MM and RR. The sum of the angles is 180° where the measure of ∠M is (4x + 20)° and the measure of ∠R is 36°.

Understand how to solve for x in a geometry problem involving adjacent supplementary angles where ∠M is (4x + 20)° and ∠R is 36°, with their sum equaling 180°. This step-by-step solution covers key concepts in algebra and geometry, ideal for students in Grades 8-10.

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