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 PP and QQ are adjacent and their sum is 180180^\circ, we can set up an equation using this information:

  1. Given: P+Q=180P + Q = 180^\circ
  2. Substitute the measures: (3x+15)+45=180(3x + 15) + 45 = 180

This equation correctly represents the setup to solve for xx.

Solution:

Simplifying the equation: 3x+15+45=1803x + 15 + 45 = 180

Therefore, the correct answer is: C. 3x+15+45=1803x + 15 + 45 = 180

Would you like more details or have any questions?


Here are some related questions to deepen your understanding:

  1. How can you solve the equation 3x+15+45=1803x + 15 + 45 = 180 to find the value of xx?
  2. What are adjacent angles, and why is their sum 180° in this context?
  3. If angle QQ were 6060^\circ instead of 4545^\circ, what would the new equation be?
  4. What is the importance of setting up an equation when solving for unknown variables?
  5. How would this problem change if the sum of PP and QQ was 9090^\circ instead of 180180^\circ?

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