Question

look at the diagram.
which equation can be used to solve for x?
$8x + 26 = 90$
$8x + 26 = 180$
$8x = 90$
$8x = 26$
solve for x.
x = \square

Explanation:

Part 1: Find the equation to solve for \( x \)

Step1: Find the supplementary angle to \( 154^\circ \)

The angle adjacent to \( 154^\circ \) on the straight line (since \( LM \) and \( MF \) are in a line? Wait, no, actually, \( \angle LMH \) is a right angle? Wait, looking at the diagram, \( \angle LMH \) is a right angle (the square at \( M \))? Wait, no, the angle between \( LM \) and \( MH \) is a right angle (90 degrees). Then, the angle between \( LM \) and \( MF \) is \( 154^\circ \), so the angle between \( MF \) and \( MH \) would be \( 180 - 154 = 26^\circ \)? Wait, no, let's re-examine. The angle at \( M \): \( LM \) is horizontal left, \( MH \) is vertical down (right angle), \( MK \) is some line, and \( MF \) is a line making \( 154^\circ \) with \( LM \). So the angle between \( LM \) and \( MF \) is \( 154^\circ \), so the angle between \( MF \) and \( MH \) (the right angle side) would be \( 154 - 90 = 64 \)? No, wait, maybe the angle between \( LM \) and \( MK \) is \( 8x \), and the angle between \( LM \) and \( MH \) is 90 degrees. Wait, the key is that the angle between \( LM \) and \( MF \) is \( 154^\circ \), so the angle between \( MF \) and the vertical (MH) is \( 154 - 90 = 64 \)? No, maybe the sum of \( 8x \) and the angle complementary to \( 154^\circ \) is 90. Wait, the correct approach: the angle between \( LM \) and \( MF \) is \( 154^\circ \), so the angle between \( LM \) and the other side (say, the angle that, when added to \( 8x \), makes 90 degrees) is \( 154 - 90 = 64 \)? No, wait, let's calculate the angle between \( MF \) and \( MH \). Since \( \angle LMH = 90^\circ \) (right angle), and \( \angle LMF = 154^\circ \), then the angle between \( MF \) and \( MH \) is \( 154^\circ - 90^\circ = 64^\circ \)? No, that doesn't make sense. Wait, maybe the angle between \( LM \) and \( MK \) is \( 8x \), and the angle between \( LM \) and \( MF \) is \( 154^\circ \), so the angle between \( MK \) and \( MF \) is \( 154 - 8x \), but that's not helpful. Wait, the problem gives options: \( 8x + 26 = 90 \), etc. Let's see: if we find that the angle complementary to \( 8x \) is \( 26^\circ \), because \( 180 - 154 = 26 \), then \( 8x + 26 = 90 \), because the right angle is 90 degrees. Ah, yes! Because \( \angle LMH = 90^\circ \) (right angle), so the sum of \( 8x \) and the angle adjacent to \( 154^\circ \) (which is \( 180 - 154 = 26^\circ \)) should equal 90 degrees. So \( 8x + 26 = 90 \). So the equation is \( 8x + 26 = 90 \).

Step2: Confirm the equation

So the correct equation is \( 8x + 26 = 90 \).

Step1: Subtract 26 from both sides

Starting with \( 8x + 26 = 90 \), subtract 26 from both sides: \( 8x = 90 - 26 \)
\( 8x = 64 \)

Step2: Divide by 8

Divide both sides by 8: \( x = \frac{64}{8} \)
\( x = 8 \)

Answer:

(for the equation): \( 8x + 26 = 90 \)

Part 2: Solve for \( x \)