Question

for each: geometry set - up/reason, substitute and solve. 21. m∠aob = 5(x + 8)°, m∠aoc=(15x + 18)°, m∠boc = 9(x - 2)°. find m∠foe.

Explanation:

Step1: Assume vertical - angle relationship or linear - pair relationship (information not fully given, assume sum of angles around a point is 360° or some angle - related property). Let's assume these angles are part of a set of angles around a point O. So, \(m\angle AOB + m\angle AOC+m\angle BOC = 180^{\circ}\) (if they form a straight - line or some relevant angle combination).

\[5(x + 8)+15x + 18+9(x - 2)=180\]

Step2: Expand the equation.

\[5x+40 + 15x+18+9x-18 = 180\]

Step3: Combine like terms.

\[(5x + 15x+9x)+(40 + 18-18)=180\]
\[29x+40 = 180\]

Step4: Solve for x.

\[29x=180 - 40\]
\[29x=140\]
\[x=\frac{140}{29}\]

Step5: Find \(m\angle FOE\) (no information about how \(\angle FOE\) is related to the other angles. If we assume no other information and just focus on the given angle expressions for now, we first need to find the value of x to substitute back into the angle expressions). But if we assume \(\angle FOE\) is related to the others in a linear - pair or vertical - angle way, we need more information. Let's just solve for x for now).

\[x=\frac{140}{29}\approx4.83\]

Answer:

\[x=\frac{140}{29}\]