Question

8.
(3x + 15)°
(2x + 50)°
____ = x
____ = m∠aec
____ = m∠bed

Explanation:

Step1: Use vertical - angles property

Vertical angles are equal. So, $\angle AEC$ and $\angle BED$ are vertical angles, and we can set up the equation $3x + 15=2x + 50$.

Step2: Solve the equation for $x$

Subtract $2x$ from both sides of the equation: $3x-2x+15=2x - 2x+50$, which simplifies to $x + 15=50$. Then subtract 15 from both sides: $x=50 - 15$, so $x = 35$.

Step3: Find the measure of $\angle AEC$

Substitute $x = 35$ into the expression for $\angle AEC$. $m\angle AEC=3x + 15=3\times35+15=105 + 15=120^{\circ}$.

Step4: Find the measure of $\angle BED$

Since $\angle BED=\angle AEC$ (vertical - angles), $m\angle BED = 120^{\circ}$.

Answer:

$x = 35$, $m\angle AEC=120^{\circ}$, $m\angle BED=120^{\circ}$