Question

solve for x: 7x + 49° 2x + 94°

Explanation:

Step1: Identify supplementary angles

The two angles \(7x + 49^\circ\) and \(2x + 94^\circ\) are supplementary (they form a linear pair), so their sum is \(180^\circ\). Thus, we set up the equation:
\(7x + 49 + 2x + 94 = 180\)

Step2: Combine like terms

Combine the \(x\)-terms and the constant terms:
\((7x + 2x) + (49 + 94) = 180\)
\(9x + 143 = 180\)

Step3: Solve for \(x\)

Subtract 143 from both sides:
\(9x = 180 - 143\)
\(9x = 37\)? Wait, no, wait, \(180 - 143 = 37\)? Wait, no, \(49 + 94 = 143\)? Wait, \(49 + 94 = 143\)? Wait, \(180 - 143 = 37\)? No, wait, I must have miscalculated. Wait, \(49 + 94 = 143\)? Wait, \(49 + 94 = 143\)? Wait, \(180 - 143 = 37\)? No, wait, no, let's recalculate:

Wait, \(7x + 49 + 2x + 94 = 180\)

Combine like terms: \(9x + 143 = 180\)

Subtract 143 from both sides: \(9x = 180 - 143 = 37\)? No, that can't be. Wait, maybe the angles are vertical angles? Wait, no, the diagram shows two angles that are adjacent and form a linear pair? Wait, no, maybe I misread the angles. Wait, maybe the angles are equal? Wait, no, the problem is about two intersecting lines, so maybe the angles are supplementary or vertical. Wait, let's check again.

Wait, maybe the angles are equal? Wait, no, the expressions are \(7x + 49\) and \(2x + 94\). Wait, maybe they are equal? Wait, no, if they are vertical angles, they would be equal. Wait, maybe the diagram is of two intersecting lines, so vertical angles are equal. Wait, maybe I made a mistake in assuming supplementary. Let's try setting them equal:

\(7x + 49 = 2x + 94\)

Subtract \(2x\) from both sides: \(5x + 49 = 94\)

Subtract 49: \(5x = 45\)

Then \(x = 9\). Ah, that makes sense. So maybe the angles are vertical angles (opposite angles when two lines intersect), so they are equal. So the correct equation is \(7x + 49 = 2x + 94\).

Step1: Set vertical angles equal

Since the angles are vertical angles (opposite when two lines intersect), they are equal:
\(7x + 49 = 2x + 94\)

Step2: Subtract \(2x\) from both sides

\(7x - 2x + 49 = 94\)
\(5x + 49 = 94\)

Step3: Subtract 49 from both sides

\(5x = 94 - 49\)
\(5x = 45\)

Step4: Divide by 5

\(x = \frac{45}{5}\)
\(x = 9\)

Answer:

9