Question

given △alg ≅ △ebr, find the value of x and y.

Explanation:

Step1: Equate corresponding angles

Since $\triangle ALG\cong\triangle EBR$, corresponding angles are equal. $\angle L=\angle E$. So, $8x = 42$.

Step2: Solve for x

Divide both sides of the equation $8x = 42$ by 8. $x=\frac{42}{8}=\frac{21}{4} = 5.25$.

Step3: Equate corresponding sides

Corresponding sides of congruent triangles are equal. $AL = EB$. So, $16=7y - 5$.

Step4: Solve for y

Add 5 to both sides of the equation: $16 + 5=7y$, which gives $21 = 7y$. Then divide both sides by 7, $y=\frac{21}{7}=3$.

Answer:

$x = 5.25$
$y = 3$