Given that $m\angle \mathrm{CED}=72°$ and $m\angle \mathrm{AEB}=7x-2°$, what is the value of $x$ if $m\angle \mathrm{CED}$ and $m\angle \mathrm{AEB}$ are complementary angles?

• A. $8$
• B. $16$
• C. $10$
• D. $12$

Answer: (B)

Verified step by step guidance

1. Recall that complementary angles are two angles whose measures add up to 90 degrees. This means we can write the equation: \(m\angle CED + m\angle AEB = 90^\circ\).
2. Substitute the given values into the equation: \$72^\circ + (7x - 2)^\circ = 90^\circ$.
3. Combine like terms on the left side: \$72 + 7x - 2 = 90$.
4. Simplify the constants: \$70 + 7x = 90$.
5. Isolate \(x\) by subtracting 70 from both sides and then dividing by 7: \$7x = 90 - 70\( and then \)x = \frac{20}{7}$.