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.5

B.25

C.35

D.90

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 \( 180^\circ \).

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.5 B.25 C.35 D.90

Explore how to solve for x when given two complementary angles, angle M and angle R, with measures (5x + 10)° and 55°, respectively. This detailed solution guides students through complementary angle properties and basic algebraic equations. Suitable for Grades 6-8.

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