Question

if (mangle fcd=(2x + 5)^{circ}) and (mangle fed=(3x - 10)^{circ}), what is the value of (x)? 19 35 37 73

Explanation:

Step1: Set the two angle - measures equal

Assume $\angle FCD=\angle FED$ (if they are congruent angles, which is a common situation in geometry problems like this). So, $2x + 5=3x - 10$.

Step2: Isolate the variable $x$

Subtract $2x$ from both sides: $2x+5 - 2x=3x - 10-2x$, which simplifies to $5=x - 10$.

Step3: Solve for $x$

Add 10 to both sides: $5 + 10=x-10 + 10$, so $x = 15$. But this is wrong. Let's assume they are supplementary angles, so $2x + 5+3x - 10=180$.

Step4: Combine like - terms

$(2x+3x)+(5 - 10)=180$, which gives $5x-5 = 180$.

Step5: Add 5 to both sides

$5x-5 + 5=180 + 5$, so $5x=185$.

Step6: Divide both sides by 5

$\frac{5x}{5}=\frac{185}{5}$, so $x = 37$.

Answer:

C. 37