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
?
A.25

B.35

C.90

D.5


Since the sum of angles \( M \) and \( R \) is \( 90^\circ \), we can set up an equation to solve for \( x \).

1. Given:
   - Measure of angle \( M = (5x + 10)^\circ \)
   - Measure of angle \( R = 55^\circ \)

2. According to the problem:
   \[
   M + R = 90^\circ
   \]

3. Substitute the values of \( M \) and \( R \):
   \[
   (5x + 10) + 55 = 90
   \]

4. Simplify the equation:
   \[
   5x + 65 = 90
   \]

5. Subtract 65 from both sides:
   \[
   5x = 25
   \]

6. Divide by 5:
   \[
   x = 5
   \]

The correct answer is:
**D. 5**

Would you like further explanation or have any questions?

---

1. What are complementary angles, and how do they relate to this problem?
2. How would the solution change if angle \( R \) were \( 45^\circ \) instead?
3. Why is it necessary to combine like terms when solving equations?
4. What are other ways to express angle relationships in geometry?
5. How can you verify that the answer for \( x \) is correct?

**Tip:** Always check your work by substituting your solution back into the original equation to ensure accuracy.

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? A.25 B.35 C.90 D.5

Learn how to find the value of x in a problem involving complementary angles where angle M is (5x + 10)° and angle R is 55°. This solution covers algebraic techniques and the complementary angle theorem, suitable for Grades 7-8.

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