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 $180^\circ$.