Math Problem Statement

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 ?

Solution

We are given that the sum of angles MM and RR is 9090^\circ, and the measures of the angles are:

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

The equation based on the sum of the angles is:

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

Substituting the given values:

(5x+10)+55=90(5x + 10) + 55 = 90

Now, solve for xx:

5x+10+55=905x + 10 + 55 = 90

Simplify the equation:

5x+65=905x + 65 = 90

Subtract 65 from both sides:

5x=255x = 25

Finally, divide by 5:

x=5x = 5

Thus, the value of xx is 55.

Would you like further details on this solution?

Here are 5 related questions to practice:

  1. If angle M=(3x+20)M = (3x + 20)^\circ and angle R=50R = 50^\circ, what is xx?
  2. What are complementary angles, and how do they relate to this problem?
  3. If angle M=(2x+30)M = (2x + 30)^\circ and angle R=(x+10)R = (x + 10)^\circ, find xx.
  4. How would the solution change if the sum of the angles was 180180^\circ instead of 9090^\circ?
  5. If angle MM increases by 55^\circ, what happens to the value of xx?

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

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Complementary Angles
Linear Equations

Formulas

Angle Sum Formula: M + R = 90°

Theorems

Complementary Angles Theorem

Suitable Grade Level

Grades 6-8