Since the sum of angles $M$ and $R$ is 90°, we can set up an equation based on the information given:

1. Let the measure of angle $M$ be $(5x + 10)^\circ$.
2. The measure of angle $R$ is $55^\circ$.
3. Since the sum of these angles is 90°, we have:

$(5x + 10) + 55 = 90$

Step-by-Step Solution

1. Simplify the equation by combining like terms: $5x + 65 = 90$

2. Subtract 65 from both sides: $5x = 25$

3. Divide both sides by 5: $x = 5$

Conclusion

The value of $x$ is 5.

Would you like further explanation on any steps, or have any other questions?

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Here are 5 questions related to this problem to explore further:

1. What would be the measure of angle $M$ once $x$ is known?
2. If angle $R$ was 60° instead of 55°, how would that affect $x$?
3. What is the definition of complementary angles?
4. How would you solve for $x$ if angle $M$ was $(5x - 10)^\circ$ instead?
5. How can you verify that two angles add up to a complementary pair?

Tip: When dealing with complementary angles, always check that the angle measures add up to 90° to confirm calculations.