owanda 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
?

We are given that the sum of angles \( M \) and \( R \) is \( 90^\circ \), and the measures of the angles are:

- Angle \( M = (5x + 10)^\circ \)
- Angle \( R = 55^\circ \)

The equation based on the sum of the angles is:

\[
M + R = 90^\circ
\]

Substituting the given values:

\[
(5x + 10) + 55 = 90
\]

Now, solve for \( x \):

\[
5x + 10 + 55 = 90
\]

Simplify the equation:

\[
5x + 65 = 90
\]

Subtract 65 from both sides:

\[
5x = 25
\]

Finally, divide by 5:

\[
x = 5
\]

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

Would you like further details on this solution?

Here are 5 related questions to practice:
1. If angle \( M = (3x + 20)^\circ \) and angle \( R = 50^\circ \), what is \( x \)?
2. What are complementary angles, and how do they relate to this problem?
3. If angle \( M = (2x + 30)^\circ \) and angle \( R = (x + 10)^\circ \), find \( x \).
4. How would the solution change if the sum of the angles was \( 180^\circ \) instead of \( 90^\circ \)?
5. If angle \( M \) increases by \( 5^\circ \), what happens to the value of \( x \)?

**Tip:** Always double-check your equation by substituting the solution back into the original problem to verify your results.

Owanda 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?

Discover how to solve for x when given complementary angles M = (5x+10)° and R = 55°. This problem explains algebraic methods and the complementary angles theorem in a step-by-step solution, suitable for students in Grades 6-8.

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