To solve for $x$, let's use the information given:

1. Since angle $M$ and angle $R$ are complementary (sum is 90°), we have: $M + R = 90^\circ$

2. We're told:

   • The measure of angle $M$ is $(5x + 10)^\circ$
   • The measure of angle $R$ is $55^\circ$

3. Substitute these values into the equation: $(5x + 10) + 55 = 90$

4. Simplify and solve for $x$: $5x + 65 = 90$ $5x = 90 - 65$ $5x = 25$ $x = 5$

Thus, the correct answer is: A. 5

Would you like further clarification or a step-by-step breakdown?

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Here are some related questions to practice:

1. If angle $M$ is $(3x + 15)^\circ$ and angle $R$ is $45^\circ$, what is $x$ if $M + R = 90^\circ$?
2. If angle $A$ measures $(4x + 20)^\circ$ and angle $B$ is complementary to angle $A$, what is $x$ if angle $B$ measures $50^\circ$?
3. What is the measure of an angle that is complementary to a $40^\circ$ angle?
4. Given two angles $A$ and $B$ such that $A = (6x - 5)^\circ$ and $B = (4x + 15)^\circ$, what value of $x$ makes them complementary?
5. If the sum of angle $P$ and angle $Q$ is $180^\circ$, and $P = (7x + 2)^\circ$, $Q = (5x - 12)^\circ$, what is $x$?

Tip: In geometry, complementary angles always add up to $90^\circ$ while supplementary angles add up to $180^\circ$.