Question

m∠aec = 2x + 30, m∠deb = 3x + 10. find m∠ceb.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle AEC$ and $\angle DEB$ are vertical angles, so $m\angle AEC=m\angle DEB$. Then we set up the equation $2x + 30=3x + 10$.

Step2: Solve the equation for x

Subtract $2x$ from both sides: $30=x + 10$. Then subtract 10 from both sides to get $x = 20$.

Step3: Find $m\angle AEC$ or $m\angle DEB$

Substitute $x = 20$ into the expression for $m\angle AEC$: $m\angle AEC=2x+30=2\times20 + 30=40 + 30=70^{\circ}$.

Step4: Use linear - pair property

$\angle AEC$ and $\angle CEB$ form a linear pair, so $m\angle AEC+m\angle CEB = 180^{\circ}$. Then $m\angle CEB=180 - m\angle AEC$.

Step5: Calculate $m\angle CEB$

$m\angle CEB=180-70 = 110^{\circ}$.

Answer:

$110$