Question

quadrilateral cdef is inscribed in circle a. if m∠c = 7x + 11° and m∠e = 6x°, what is the measure of ∠e?

Explanation:

Step1: Use the property of cyclic quadrilaterals

In a cyclic quadrilateral, the sum of opposite angles is \(180^{\circ}\). So, \(m\angle C + m\angle E=180^{\circ}\).

Step2: Substitute the given expressions

Substitute \(m\angle C = 7x + 11\) and \(m\angle E=6x\) into the equation \(7x + 11+6x=180\).

Step3: Solve for \(x\)

Combine like - terms: \(13x+11 = 180\).
Subtract 11 from both sides: \(13x=180 - 11=169\).
Divide both sides by 13: \(x=\frac{169}{13}=13\).

Step4: Find \(m\angle E\)

Since \(m\angle E = 6x\), substitute \(x = 13\) into it. So, \(m\angle E=6\times13 = 78^{\circ}\).

Answer:

\(78^{\circ}\)