Question

solve for the value of e.
(4e+6)°
(9e-8)°
answer
e =
submit answer

Explanation:

Step1: Identify angle relationship

The two angles \((9e - 8)^\circ\) and \((4e + 6)^\circ\) are supplementary (they form a linear pair), so their sum is \(180^\circ\)? Wait, no, wait. Wait, looking at the diagram, actually, wait—wait, no, maybe they are complementary? Wait, no, the diagram shows a straight line? Wait, no, the two angles are adjacent and form a linear pair? Wait, no, wait, maybe I misread. Wait, no, the two angles: \((9e - 8)\) and \((4e + 6)\) — wait, no, actually, maybe they are supplementary? Wait, no, wait, let's check again. Wait, the diagram: there's a straight line, and a ray in between, creating two angles. Wait, no, actually, wait, maybe the two angles are supplementary? Wait, no, wait, no—wait, no, the sum of the two angles should be \(180^\circ\)? Wait, no, wait, no, maybe I made a mistake. Wait, no, let's look again. The two angles are \((9e - 8)^\circ\) and \((4e + 6)^\circ\), and they are adjacent, forming a linear pair, so their sum is \(180^\circ\)? Wait, no, wait, no—wait, no, maybe they are supplementary? Wait, no, wait, no, let's calculate. Wait, no, wait, maybe the two angles are supplementary? Wait, no, wait, let's set up the equation: \((9e - 8) + (4e + 6) = 180\)? Wait, no, that can't be, because if we solve that, \(13e - 2 = 180\), \(13e = 182\), \(e = 14\). But wait, maybe I misread the diagram. Wait, no, maybe the two angles are complementary? Wait, no, the diagram shows a straight line? Wait, no, maybe the two angles are adjacent and form a linear pair, so their sum is \(180^\circ\). Wait, let's check the equation again.

Wait, let's do the step properly.

Step1: Determine angle sum

The two angles \((9e - 8)^\circ\) and \((4e + 6)^\circ\) are supplementary (they form a linear pair), so:

\((9e - 8) + (4e + 6) = 180\)

Step2: Simplify the equation

Combine like terms:

\(9e + 4e - 8 + 6 = 180\)

\(13e - 2 = 180\)

Step3: Solve for \(e\)

Add 2 to both sides:

\(13e = 180 + 2\)

\(13e = 182\)

Divide both sides by 13:

\(e = \frac{182}{13}\)

\(e = 14\)

Wait, but let's verify. If \(e = 14\), then \(9e - 8 = 9*14 - 8 = 126 - 8 = 118\), and \(4e + 6 = 4*14 + 6 = 56 + 6 = 62\). Then \(118 + 62 = 180\), which is correct for a linear pair. So that works.

Answer:

\(e = 14\)