Question

In triangle, W, X, Y, comma△WXY, start overline, X, Y, end overline, \cong, start overline, W, X, end overline
XY
≅
WX
and m, angle, X, equals, 88, degrees, .m∠X=88
∘
. Find m, angle, W, .m∠W

Answer 1

In triangle \( \triangle WXY \), you have \( \overline{XY} \cong \overline{WX} \) and \( m\angle X = 88^\circ \). Since \( \overline{XY} \cong \overline{WX} \), this indicates that triangle \( WXY \) is isosceles with \( \overline{XY} \) and \( \overline{WX} \) being the two equal sides.

In any triangle, the sum of the angles is \( 180^\circ \). Let's denote \( m\angle W \) as \( x \) and \( m\angle Y \) will also be \( x \) since \( \triangle WXY \) is isosceles with the two angles opposite the equal sides being equal.

The angle sum equation for triangle \( WXY \) is:

\[
m\angle W + m\angle Y + m\angle X = 180^\circ
\]

Substituting what we have:

\[
x + x + 88^\circ = 180^\circ
\]

Simplifying this gives:

\[
2x + 88^\circ = 180^\circ
\]

Subtracting \( 88^\circ \) from both sides:

\[
2x = 180^\circ - 88^\circ
\]
\[
2x = 92^\circ
\]

Dividing by 2:

\[
x = 46^\circ
\]

Thus, \( m\angle W = 46^\circ \). Therefore, the measure of angle \( W \) is:

\[
\boxed{46^\circ}
\]