Question

11.
c
(x + 12)°
(3x + 2)°
e
d
___ = x
___ = m∠bec

Explanation:

Step1: Set up equation based on angle - sum

Since $\angle BEC+\angle CED = 90^{\circ}$ (right - angle), we have the equation $(x + 12)+(3x+2)=90$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $x+3x+12 + 2=90$, which simplifies to $4x+14 = 90$.

Step3: Isolate the variable term

Subtract 14 from both sides of the equation: $4x=90 - 14$, so $4x=76$.

Step4: Solve for $x$

Divide both sides by 4: $x=\frac{76}{4}=19$.

Step5: Find $m\angle BEC$

Substitute $x = 19$ into the expression for $\angle BEC$. $m\angle BEC=x + 12$. So $m\angle BEC=19+12=31^{\circ}$.

Answer:

$x = 19$, $m\angle BEC=31^{\circ}$