Math Problem Statement

∠1 and ∠2 are complementary angles. If m∠1 = (6x + 18)° and m∠2 = (3x − 9)°, find the measure of ∠1.

Solution

The problem states that ∠1 and ∠2 are complementary angles, meaning their sum is 90°. We're given:

  • m∠1 = (6x + 18)°
  • m∠2 = (3x − 9)°

Since complementary angles sum to 90°, we can set up the equation:

m1+m2=90°m∠1 + m∠2 = 90°

Substitute the expressions for m∠1 and m∠2:

(6x+18)+(3x9)=90(6x + 18) + (3x − 9) = 90

Now, combine like terms:

6x+3x+189=906x + 3x + 18 − 9 = 90 9x+9=909x + 9 = 90

Solve for xx:

9x=9099x = 90 − 9 9x=819x = 81 x=819=9x = \frac{81}{9} = 9

Now that we know x=9x = 9, substitute this value back into the expression for m∠1:

m1=6x+18=6(9)+18=54+18=72°m∠1 = 6x + 18 = 6(9) + 18 = 54 + 18 = 72°

Therefore, the measure of ∠1 is 72°.

Would you like more details or have any questions?

Here are some related questions you might consider:

  1. What would happen if the angles were supplementary instead of complementary?
  2. How would the solution change if m∠1 were (7x + 10)° and m∠2 were (2x - 5)°?
  3. Can two angles both be 45° and still satisfy the given conditions?
  4. What if the sum of the angles was 180° instead of 90°?
  5. How would you verify the solution by substituting back into both angle equations?

Tip: Always double-check the angle sum when working with complementary or supplementary angles to ensure the correct relationship is used.

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Math Problem Analysis

Mathematical Concepts

Algebra
Complementary Angles

Formulas

m∠1 + m∠2 = 90°

Theorems

Complementary Angle Theorem

Suitable Grade Level

Grades 7-9