Question

given that △mas ≅ △ner,
a. solve for the value of x.
b. solve for the value of y.

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle MAS\cong\triangle NER\), corresponding angles are equal. So, \(16x = 112\) (corresponding angles).
$$16x=112$$

Step2: Solve for \(x\)

Divide both sides of the equation \(16x = 112\) by \(16\).
$$x=\frac{112}{16}=7$$

Step3: Use the property of congruent triangles for side - angle relationship

Corresponding sides are equal. So, \(3x + 5y=41\) (corresponding sides). Substitute \(x = 7\) into the equation \(3x+5y = 41\).
$$3\times7+5y=41$$
$$21 + 5y=41$$

Step4: Solve for \(y\)

Subtract \(21\) from both sides: \(5y=41 - 21\).
$$5y=20$$
Divide both sides by \(5\): \(y=\frac{20}{5}=4\)

Answer:

A. \(x = 7\)
B. \(y = 4\)