Question

if m∠cfe=(2x + 6)° and m∠cde=(2x - 2)°, what is the value of x? quadrilateral cdef is inscribed in circle a.

Explanation:

Step1: Recall property of cyclic quadrilateral

Opposite angles of a cyclic quadrilateral are supplementary, so \(m\angle CFE+m\angle CDE = 180^{\circ}\).

Step2: Substitute angle - expressions

Substitute \(m\angle CFE=(2x + 6)^{\circ}\) and \(m\angle CDE=(2x-2)^{\circ}\) into the equation: \((2x + 6)+(2x-2)=180\).

Step3: Simplify the left - hand side

Combine like terms: \(2x+2x+6 - 2=180\), which simplifies to \(4x + 4=180\).

Step4: Isolate the variable term

Subtract 4 from both sides: \(4x=180 - 4\), so \(4x=176\).

Step5: Solve for x

Divide both sides by 4: \(x=\frac{176}{4}=44\).

Answer:

\(x = 44\)