Question

what is the measure of ∠abc? 131° 53° a. 127° b. 88° c. 131° d. 92°

Explanation:

Step1: Recall the property of angles formed by intersecting chords in a circle

The measure of an angle formed by two intersecting chords in a circle is half the sum of the measures of the intercepted arcs. Here, \(\angle ABC\) is an angle formed by two intersecting chords \(AC\) and \(DE\). The intercepted arcs are \(131^{\circ}\) and \(53^{\circ}\).

Step2: Apply the formula

The formula for the measure of the angle \(\theta\) formed by two - intersecting chords is \(\theta=\frac{1}{2}(m_1 + m_2)\), where \(m_1\) and \(m_2\) are the measures of the intercepted arcs. Substitute \(m_1 = 131^{\circ}\) and \(m_2=53^{\circ}\) into the formula: \(\angle ABC=\frac{1}{2}(131 + 53)\).

Step3: Calculate the value

First, add the values inside the parentheses: \(131+53 = 184\). Then, divide by 2: \(\frac{184}{2}=92^{\circ}\).

Answer:

D. \(92^{\circ}\)