Question

what is x? I solved it but got a really long line of decimals, so I'm not sure if I solved it right, it's attached below.

Answer 1

ANSWER

m∠2 = 137°

EXPLANATION

By the angles of intersecting chords theorem, we have,

$m\angle2=\frac{1}{2}(mVW+mZX)$

We don't know the measure of these two arcs, but we do know the measures of arcs VX and WZ. The sum of all the measures of consecutive arcs is 360°, so,

$mVW+mWZ+mZX+mVX=360$

Group them,

$(mVW+mZX)+(mWZ+mVX)=360$

Solve for (mVW+mZX),

$(mVW+mZX)=360-\left(mWZ+mVX\right)$

Replace the known values,

$(mVW+mZX)=360-(38+48)=360-86=274$

Finally,

$m\operatorname{\angle}2=\frac{1}{2}(mVW+mZX)=\frac{1}{2}\cdot274\degree=137\degree$

Hence, the measure of angle 2 is 137°.