Question

1. if ef bisects ∠ceb, m∠cef=(7x + 21)° and m∠feb=(10x - 3)°, find the measure of ∠deb.

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{EF}$ bisects $\angle CEB$, we have $m\angle CEF=m\angle FEB$. So, $7x + 21=10x-3$.

Step2: Solve the equation for $x$

Subtract $7x$ from both sides: $21 = 10x-7x - 3$. Then $21=3x - 3$. Add 3 to both sides: $21 + 3=3x$, so $24 = 3x$. Divide both sides by 3: $x = 8$.

Step3: Find the measure of $\angle FEB$

Substitute $x = 8$ into the expression for $m\angle FEB$. $m\angle FEB=(10x - 3)^{\circ}=(10\times8-3)^{\circ}=77^{\circ}$.

Step4: Find the measure of $\angle DEB$

$\angle DEB$ and $\angle CEB$ are vertical - angles, and $\angle CEB = 2\angle FEB$. So $m\angle DEB=2m\angle FEB$. Since $m\angle FEB = 77^{\circ}$, then $m\angle DEB = 154^{\circ}$.

Answer:

$154^{\circ}$