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

What is the value of x
?

Since angles \( M \) and \( R \) are adjacent and their sum is \( 180^\circ \), they form a straight angle. We can set up the equation:

\[
\text{Measure of } \angle M + \text{Measure of } \angle R = 180^\circ
\]

Given:
- Measure of \( \angle M = (4x + 20)^\circ \)
- Measure of \( \angle R = 36^\circ \)

So, we substitute and solve for \( x \):

\[
(4x + 20) + 36 = 180
\]

Combine terms:

\[
4x + 56 = 180
\]

Subtract 56 from both sides:

\[
4x = 124
\]

Divide by 4:

\[
x = 31
\]

### Answer:
The value of \( x \) is \( 31 \).

Would you like a step-by-step breakdown of the solution or have any other questions?

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Here are some related questions:
1. How would the value of \( x \) change if the measure of \( \angle R \) was different?
2. What is the value of \( \angle M \) when \( x = 31 \)?
3. What are adjacent angles, and why do they sum to \( 180^\circ \) in this case?
4. How could you determine if two angles are complementary or supplementary?
5. Can the measure of \( \angle M \) be greater than \( 144^\circ \)? Why or why not?

**Tip:** For any adjacent angles forming a straight line, always remember they are supplementary, summing to \( 180^\circ \).

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

Learn how to find the value of x in a problem involving adjacent angles ∠M and ∠R that sum to 180°. This solution uses algebraic methods and the supplementary angles theorem to solve for x when ∠M = (4x + 20)° and ∠R = 36°. Suitable for students in Grades 6-8.

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