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

Explanation:

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

Vertical angles formed by two intersecting chords in a circle have a measure related to the arcs they intercept. The measure of an angle formed by two intersecting chords in a circle is half the sum of the measures of the intercepted arcs. Also, vertical angles are equal.

Step2: Identify the intercepted arcs

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

Step3: Calculate the measure of ∠2

The formula for the measure of an angle formed by two intersecting chords is $m\angle=\frac{1}{2}(x + y)$, where $x$ and $y$ are the measures of the intercepted arcs. Here, $x = 133^{\circ}$ and $y=147^{\circ}$. So, $m\angle2=\frac{1}{2}(133 + 147)$. First, calculate the sum inside the parentheses: $133+147 = 280^{\circ}$. Then, divide by 2: $\frac{280}{2}=140^{\circ}$.

Answer:

$140^{\circ}$