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

Since angles \( P \) and \( Q \) are adjacent and their sum is \( 180^\circ \), we can set up an equation using this information:

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

This equation correctly represents the setup to solve for \( x \).

### Solution:
Simplifying the equation:
\[
3x + 15 + 45 = 180
\]

Therefore, the correct answer is:
**C. \( 3x + 15 + 45 = 180 \)**

Would you like more details or have any questions?

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Here are some related questions to deepen your understanding:

1. How can you solve the equation \( 3x + 15 + 45 = 180 \) to find the value of \( x \)?
2. What are adjacent angles, and why is their sum 180° in this context?
3. If angle \( Q \) were \( 60^\circ \) instead of \( 45^\circ \), 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 \( P \) and \( Q \) was \( 90^\circ \) instead of \( 180^\circ \)?

**Tip**: Always carefully verify the conditions given, such as the sum of the angles, to select the right equation.

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) = 90

Discover how to solve for x in a problem involving two adjacent angles, P and Q, where P is represented as (3x + 15)° and Q as 45°. This problem explores key concepts in geometry and algebra, providing a step-by-step guide for students in Grades 6-8.

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