Towanda has angle MM and angle RR. Their sum is 90°90°.
• The measure of angle MM is (5x+10)°(5x+10)°.
• The measure of angle RR is 55°55°.
What is the value of xx?

Since the sum of angle \( M \) and angle \( R \) is \( 90^\circ \), we can set up an equation based on the information given.

1. Let angle \( M = (5x + 10)^\circ \).
2. Let angle \( R = 55^\circ \).

Since the angles are complementary (sum to \( 90^\circ \)), we have:
\[
(5x + 10) + 55 = 90
\]

Now, we can solve for \( x \):
1. Simplify the equation:
   \[
   5x + 65 = 90
   \]
2. Subtract \( 65 \) from both sides:
   \[
   5x = 25
   \]
3. Divide by \( 5 \) to isolate \( x \):
   \[
   x = 5
   \]

Therefore, the value of \( x \) is \( 5 \).

Would you like more details on this solution, or do you have any questions?

Here are some related questions to consider:
1. What if the measure of angle \( R \) were different? How would \( x \) change?
2. What if the sum of angles \( M \) and \( R \) was a different angle measure?
3. How would you solve for \( x \) if angle \( M \) were given in terms of \( x^2 \)?
4. Can you apply similar logic to find unknowns in triangles?
5. How would the equation look if \( M \) and \( R \) were supplementary instead of complementary?

**Tip:** Remember that complementary angles always add up to \( 90^\circ \), while supplementary angles add up to \( 180^\circ \).

Towanda has angle M and angle R. Their sum is 90°. The measure of angle M is (5x+10)°. The measure of angle R is 55°. What is the value of x?

Learn how to solve for x when given two complementary angles, (5x + 10)° and 55°, that add up to 90°. This step-by-step solution covers core concepts in algebra and geometry, ideal for students in Grades 6-8.

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