Question

1. find the value of x. state the angle - pair relationship used.

a. relationship:
b. x = (show work)
c. find the m∠fed.
d. find the m∠cde.

Explanation:

Step1: Identify angle - pair relationship

Assume $\angle FED$ and $\angle CDE$ are alternate - interior angles (since $AB\parallel FE\parallel CD$). Alternate - interior angles are equal.

Step2: Set up equation

Set $3x + 7=10x-22$.

Step3: Solve for x

Subtract $3x$ from both sides: $7 = 10x-3x - 22$, which simplifies to $7=7x - 22$.
Add 22 to both sides: $7 + 22=7x$, so $29 = 7x$.
Then $x=\frac{29}{7}\approx4.14$.

Step4: Find $m\angle FED$

Substitute $x = \frac{29}{7}$ into the expression for $\angle FED$: $m\angle FED=3x + 7=3\times\frac{29}{7}+7=\frac{87}{7}+7=\frac{87 + 49}{7}=\frac{136}{7}\approx19.43^{\circ}$.

Step5: Find $m\angle CDE$

Since $\angle FED=\angle CDE$ (alternate - interior angles), $m\angle CDE=\frac{136}{7}\approx19.43^{\circ}$.

Answer:

a. Relationship: Alternate - interior angles
b. $x=\frac{29}{7}$
c. $m\angle FED=\frac{136}{7}$
d. $m\angle CDE=\frac{136}{7}$