Question

in circle z, what is m∠2? 147° 133° 70° 140°

Explanation:

Step1: Recall the property of vertical - angles and arc - angle relationships

Vertical angles formed by two intersecting chords in a circle have measures related to the arcs they intercept. Angle 1 and angle 2 are vertical angles. The measure of an angle formed by two intersecting chords in a circle is given by $\frac{1}{2}$ the sum of the measures of the intercepted arcs.

Step2: Identify the intercepted arcs

The arcs intercepted by angle 2 are 133° and 147°.

Step3: Calculate the measure of angle 2

Using the formula $m\angle2=\frac{1}{2}(133 + 147)$. First, find the sum of the arcs: $133+147 = 280$. Then, $m\angle2=\frac{1}{2}\times280=140^{\circ}$.

Answer:

$140^{\circ}$