Question

solve for x:
diagram with angles ( 9x + 184^circ ) (green) and ( 7x + 156^circ ) (blue) formed by intersecting lines
( x = square )

Explanation:

Step1: Identify supplementary angles

The two angles \( 9x + 184^\circ \) and \( 7x + 156^\circ \) are supplementary (they form a linear pair), so their sum is \( 180^\circ \).
\[
(9x + 184) + (7x + 156) = 180
\]

Step2: Combine like terms

Combine the \( x \)-terms and the constant terms:
\[
9x + 7x + 184 + 156 = 180
\]
\[
16x + 340 = 180
\]

Step3: Solve for \( x \)

Subtract \( 340 \) from both sides:
\[
16x = 180 - 340
\]
\[
16x = -160
\]
Divide both sides by \( 16 \):
\[
x = \frac{-160}{16}
\]
\[
x = -10
\]
Wait, there was a mistake in the previous calculation. Let's correct it.

Step1: Correct supplementary angles setup

Wait, actually, the two angles are vertical angles? No, looking at the diagram, they are adjacent and form a linear pair? Wait, no, maybe I misread. Wait, the two angles: \( 9x + 184 \) and \( 7x + 156 \). Wait, maybe they are supplementary? Wait, no, let's check again.

Wait, maybe the angles are equal? No, that can't be. Wait, maybe the sum is \( 180^\circ \). Wait, let's recalculate:

\[
9x + 184 + 7x + 156 = 180
\]
\[
16x + 340 = 180
\]
\[
16x = 180 - 340
\]
\[
16x = -160
\]
\[
x = -10
\]
Wait, that gives \( x = -10 \). Let's check:

For \( x = -10 \), \( 9x + 184 = 9(-10) + 184 = -90 + 184 = 94^\circ \)

\( 7x + 156 = 7(-10) + 156 = -70 + 156 = 86^\circ \)

And \( 94 + 86 = 180^\circ \), which is correct. So the correct answer is \( x = -10 \).

Wait, I made a mistake earlier in the final calculation. Let's redo Step3:

Step3: Solve for \( x \)

Subtract \( 340 \) from both sides:
\[
16x = 180 - 340
\]
\[
16x = -160
\]
Divide both sides by \( 16 \):
\[
x = \frac{-160}{16} = -10
\]

So the correct answer is \( x = -10 \).

Answer:

\( x = -1 \)