Math Problem Statement
Maria is studying two adjacent angles, P and Q. The sum of the angles is 180°, where the measure of angle P is (3x + 15)° and the measure of angle Q is 45°.
Which equation could be used to find x? A.3x + 15 = 45 B.3x + 15 + 45 = 90 C.3x + 15 + 45 = 180 D.45(3x + 15) = 90Maria is studying two adjacent angles, P and Q. The sum of the angles is 180°, where the measure of angle P is (3x + 15)° and the measure of angle Q is 45°.
Which equation could be used to find x? A.3x + 15 = 45 B.3x + 15 + 45 = 90 C.3x + 15 + 45 = 180 D.45(3x + 15) = 90
Solution
Since angles and are adjacent and their sum is , we can set up an equation using this information:
- Given:
- Substitute the measures:
This equation correctly represents the setup to solve for .
Solution:
Simplifying the equation:
Therefore, the correct answer is: C.
Would you like more details or have any questions?
Here are some related questions to deepen your understanding:
- How can you solve the equation to find the value of ?
- What are adjacent angles, and why is their sum 180° in this context?
- If angle were instead of , what would the new equation be?
- What is the importance of setting up an equation when solving for unknown variables?
- How would this problem change if the sum of and was instead of ?
Tip: Always carefully verify the conditions given, such as the sum of the angles, to select the right equation.
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Math Problem Analysis
Mathematical Concepts
Geometry
Algebra
Adjacent Angles
Linear Equations
Formulas
P + Q = 180° (Sum of adjacent angles)
Theorems
Adjacent Angles Theorem
Suitable Grade Level
Grades 6-8