Question

1. if m∠abc=(5x + 7)°, m∠cbe=(2x + 6)°, m∠abe = 41° what is x?

Explanation:

Step1: Use angle - addition postulate

Since $\angle ABE=\angle ABC+\angle CBE$, we can set up the equation $(5x + 7)+(2x+6)=41$.

Step2: Combine like - terms

Combining the $x$ terms and the constant terms on the left - hand side gives $5x+2x+7 + 6=41$, which simplifies to $7x+13 = 41$.

Step3: Isolate the variable term

Subtract 13 from both sides of the equation: $7x+13−13=41−13$, resulting in $7x=28$.

Step4: Solve for x

Divide both sides of the equation by 7: $\frac{7x}{7}=\frac{28}{7}$, so $x = 4$.

Answer:

$x = 4$