Question

1. in the diagram shown, ∠abc is a right angle. if m∠ebc = 39° and m∠abe = 3(x + 4), then find the value of x algebraically. show how you found your answer.

Explanation:

Step1: Set up equation

Since $\angle ABC$ is a right - angle ($m\angle ABC = 90^{\circ}$) and $\angle ABC=\angle ABE+\angle EBC$, we have the equation $3(x + 4)+39=90$.

Step2: Simplify left - hand side

First, expand $3(x + 4)$ to get $3x+12$. Then the equation becomes $3x+12 + 39=90$, which simplifies to $3x+51 = 90$.

Step3: Isolate the term with $x$

Subtract 51 from both sides of the equation: $3x=90 - 51$, so $3x=39$.

Step4: Solve for $x$

Divide both sides of the equation by 3: $x=\frac{39}{3}=13$.

Answer:

$x = 13$