Question

1.) ∠bea = 4x+18 and ∠aed = 2x+48. find the measure of x.

Explanation:

Step1: Identify angle relationship

$\angle BEA$ and $\angle AED$ are linear - pair angles, so $\angle BEA+\angle AED = 180^{\circ}$.

Step2: Substitute angle expressions

$(4x + 18)+(2x+48)=180$.

Step3: Combine like - terms

$4x+2x+18 + 48=180$, which simplifies to $6x+66 = 180$.

Step4: Isolate the variable term

Subtract 66 from both sides: $6x=180 - 66$, so $6x=114$.

Step5: Solve for x

Divide both sides by 6: $x=\frac{114}{6}=19$.

Answer:

$x = 19$