Question

ure to find x?
there is a straight line with a ray forming an angle. one angle is ( 3x + 1^circ ), the other is ( 52^circ ).

Explanation:

Step1: Recognize supplementary angles

The two angles \(3x + 1^\circ\) and \(52^\circ\) form a linear pair, so they are supplementary (sum to \(180^\circ\)).
\[
(3x + 1) + 52 = 180
\]

Step2: Simplify the equation

Combine like terms:
\[
3x + 53 = 180
\]

Step3: Solve for \(x\)

Subtract 53 from both sides:
\[
3x = 180 - 53
\]
\[
3x = 127
\]
Divide both sides by 3:
\[
x = \frac{127}{3} \approx 42.33
\]
Wait, there's a mistake. Let's correct Step 1. The sum of a linear pair is \(180^\circ\), so:

Step1: Correct equation setup

\(3x + 1 + 52 = 180\) (since they are supplementary)
\[
3x + 53 = 180
\]

Step2: Subtract 53 from both sides

\[
3x = 180 - 53
\]
\[
3x = 127
\]
Wait, no, 180 - 53 is 127? Wait, 180 - 50 is 130, minus 3 is 127. Then divide by 3: \(x = \frac{127}{3} \approx 42.33\)? Wait, maybe I made a mistake in the angle sum. Wait, no, linear pair is 180 degrees. Wait, let's check again.

Wait, the two angles are \(3x + 1\) and \(52^\circ\), and they form a straight line, so their sum is \(180^\circ\). So:

\(3x + 1 + 52 = 180\)

Combine like terms: \(3x + 53 = 180\)

Subtract 53 from both sides: \(3x = 180 - 53 = 127\)

Then \(x = \frac{127}{3} \approx 42.33\)? Wait, that seems odd. Wait, maybe the angle is \(3x - 1\) or something? Wait, no, the original problem says \(3x + 1^\circ\). Wait, maybe I miscalculated 180 - 53. 53 + 127 is 180? 50 + 127 is 177, plus 3 is 180. Yes. So \(x = \frac{127}{3} \approx 42.33\). But maybe the problem has a typo, or I misread. Wait, maybe the angle is \(3x - 1\)? No, the user wrote \(3x + 1^\circ\). So the calculation is correct.

Wait, let's do it again:

1. Linear pair: sum to \(180^\circ\). So \(3x + 1 + 52 = 180\)
2. \(3x + 53 = 180\)
3. \(3x = 180 - 53 = 127\)
4. \(x = \frac{127}{3} \approx 42.33\)

But maybe the problem is \(3x - 1\)? Let's check. If it's \(3x - 1\), then \(3x - 1 + 52 = 180\) => \(3x + 51 = 180\) => \(3x = 129\) => \(x = 43\). That's a whole number. Maybe a typo in the problem, but as per the given, it's \(3x + 1\). So the answer is \(x = \frac{127}{3}\) or approximately 42.33. But maybe I made a mistake. Wait, 3x + 1 + 52 = 180. So 3x = 180 - 53 = 127. So x = 127/3 ≈ 42.33.

Answer:

\(x = \frac{127}{3} \approx 42.33\) (or if there's a typo and it's \(3x - 1\), then \(x = 43\), but based on the given, it's \(\frac{127}{3}\))