Question

question 7 (multiple choice worth 1 points)
(07.02 mc)
quadrilateral cdef is inscribed in circle a. if m∠c = 9x° and m∠e = 7x + 4°, what is the measure of ∠e?
○ 95°
○ 99°
○ 81°
○ 85°

Explanation:

Step1: Use property of cyclic quadrilaterals

In a cyclic quadrilateral, the sum of opposite angles is \(180^{\circ}\). So, \(m\angle C + m\angle E=180^{\circ}\). Given \(m\angle C = 9x^{\circ}\) and \(m\angle E=(7x + 4)^{\circ}\), we have the equation \(9x+7x + 4=180\).

Step2: Solve the equation for \(x\)

Combine like - terms: \(16x+4 = 180\). Subtract 4 from both sides: \(16x=180 - 4=176\). Then divide both sides by 16: \(x=\frac{176}{16}=11\).

Step3: Find \(m\angle E\)

Substitute \(x = 11\) into the expression for \(m\angle E\). \(m\angle E=7x+4\). So \(m\angle E=7\times11 + 4=77+4=81^{\circ}\).

Answer:

\(81^{\circ}\)