Question

geometry module...
in the diagram above ( \triangle fgh cong \triangle str ). using the
information on given sides and angles, find the
values of ( x ) and ( y ).
( x = )
( y = )

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle FGH\cong\triangle STR\), corresponding angles and sides are equal.

Step2: Find the value of \(x\)

Assume in \(\triangle FGH\) and \(\triangle STR\), the angle corresponding to \(x\) is \(96^{\circ}\) (by the property of congruent triangles, corresponding angles are equal). So \(x = 96\).

Step3: Find the value of \(y\)

Assume the side corresponding to \(3y + 15\) has a length of \(42\) (from the congruent triangle property, corresponding sides are equal). Then \(3y+15 = 42\). Subtract \(15\) from both sides: \(3y=42 - 15=27\). Divide both sides by \(3\): \(y=\frac{27}{3}=9\).

Answer:

\(x = 96\), \(y = 9\)