Question

what is ( moverarc{tv} )?
there is a circle with center at the intersection of three radii. the arc from v to u is labeled ( 140^circ ), the arc from u to t is labeled ( 90^circ ), and we need to find ( moverarc{tv} ).
( moverarc{tv} = square^circ )

Explanation:

Step1: Recall total circle degrees

A full circle has \( 360^\circ \).

Step2: Sum known arcs, subtract from 360

Known arcs: \( 140^\circ \) (VU) and \( 90^\circ \) (UT). Let \( m\overarc{TV} = x \). Then \( 140 + 90 + x = 360 \).
Simplify: \( 230 + x = 360 \). Subtract 230: \( x = 360 - 230 = 130 \).

Answer:

\( 130 \)