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. $\angle A=\angle E = 42^{\circ}$, $\angle L=\angle B = 56^{\circ}$, $\angle G=\angle R=82^{\circ}$. Also, for $\angle L = 56^{\circ}$, we have $8x = 56$.
$8x=56$

Step2: Solve for x

Divide both sides of the equation $8x = 56$ by 8.
$x=\frac{56}{8}=7$

Step3: Equate corresponding sides

Corresponding sides of congruent triangles are equal. $AL = EB$. Given $AL = 16$ and $EB=7y - 5$, we set up the equation $7y-5 = 16$.
$7y-5 = 16$

Step4: Solve for y

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

Answer:

$x = 7$
$y = 3$