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:
Substitute the expressions for m∠1 and m∠2:
Now, combine like terms:
Solve for :
Now that we know , substitute this value back into the expression for m∠1:
Therefore, the measure of ∠1 is 72°.
Would you like more details or have any questions?
Here are some related questions you might consider:
- What would happen if the angles were supplementary instead of complementary?
- How would the solution change if m∠1 were (7x + 10)° and m∠2 were (2x - 5)°?
- Can two angles both be 45° and still satisfy the given conditions?
- What if the sum of the angles was 180° instead of 90°?
- 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