Question

(a) in the figure below, m\\(\overarc{vw}\\)=81° and m\\(\overarc{xy}\\)=115°. find m\\(\angle vzw\\).
m\\(\angle vzw\\)=\\(\boxed{}\\)°

Explanation:

Step1: Recall the theorem for angle formed by two chords

The measure of an angle formed by two intersecting chords is equal to half the sum of the measures of the intercepted arcs. So, \( m\angle VZW=\frac{1}{2}(m\widehat{VW} + m\widehat{XY}) \).

Step2: Substitute the given arc measures

We know \( m\widehat{VW} = 81^\circ \) and \( m\widehat{XY}=115^\circ \). Substitute these values into the formula: \( m\angle VZW=\frac{1}{2}(81^\circ + 115^\circ) \).

Step3: Calculate the sum and then half of it

First, calculate the sum inside the parentheses: \( 81^\circ+115^\circ = 196^\circ \). Then, take half of that: \( \frac{1}{2}\times196^\circ = 98^\circ \).

Answer:

\( 98 \)