Question

in the diagram, abgh ≅ cdef.

1. identify all pairs of congruent corresponding parts.
2. find the value of x.

Explanation:

Step1: Use congruent property

Since \(ABGH\cong CDEF\), then \(\angle H=\angle E\).

Step2: Set up equation

We know that \(\angle H=(4x + 5)^{\circ}\) and \(\angle E = 75^{\circ}\). So, \(4x+5=75\).

Step3: Solve the equation

Subtract \(5\) from both sides: \(4x=75 - 5\), \(4x=70\).
Divide both sides by \(4\): \(x=\frac{70}{4}=17.5\).

Answer:

\(x = 17.5\)