Question

two chords intersect inside a circle, forming vertical angles. the intercepted arc measures for one pair of vertical angles are 32° and 56°. what is the measure of each of these vertical angles? show your work. drag the correct expressions into the boxes to correctly solve for x. show hints x = x = 1/2 x = 1/2 (32° + 56°) (24°) (32° - 56°) (-24°) 12° 44° (52° - 36°) (88°) check

Explanation:

Step1: Recall angle - chord theorem

The measure of a vertical angle formed by two chords intersecting inside a circle is half the sum of the measures of the intercepted arcs. Let the two intercepted arcs be \(a = 32^{\circ}\) and \(b = 56^{\circ}\). The measure of the vertical angle \(x=\frac{1}{2}(a + b)\).

Step2: Calculate the value of \(x\)

Substitute \(a = 32^{\circ}\) and \(b = 56^{\circ}\) into the formula \(x=\frac{1}{2}(32^{\circ}+ 56^{\circ})\). First, calculate the sum inside the parentheses: \(32^{\circ}+56^{\circ}=88^{\circ}\). Then, find half of the sum: \(x = 44^{\circ}\).

Answer:

\(44^{\circ}\)