Question

what is $moverarc{uv}$?
there is a circle with center at the intersection point of three radii. the radii are to points w, v, and u. the arc from w to v is labeled 90°, the arc from u to the other side (not w or v) is labeled 140°, and we need to find $moverarc{uv}$. there is a submit button below the input box for the answer.

Explanation:

Step1: Recall circle angle sum

A full circle is \( 360^\circ \). Let \( m\widehat{UV} = x \). The known arcs are \( 140^\circ \) and \( 90^\circ \).

Step2: Set up equation

Sum of arcs: \( 140^\circ + 90^\circ + x = 360^\circ \).

Step3: Solve for \( x \)

Calculate \( 140 + 90 = 230 \). Then \( x = 360 - 230 = 130 \).

Answer:

\( 130 \)