Question

if m∠sxt = 142°, then what is m∠uxs?
diagram of intersecting lines with points t, x, r, s, y, w, u, v and angles labeled 1, 2, 3, 4, 5, 6
answer attempt 1 out of 2
m∠uxs = input box°
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Explanation:

Step1: Identify supplementary angles

Angles \( \angle SXT \) and \( \angle UXS \) are supplementary (they form a linear pair), so their measures add up to \( 180^\circ \).
\[
m\angle SXT + m\angle UXS = 180^\circ
\]

Step2: Substitute known value

We know \( m\angle SXT = 142^\circ \), so substitute into the equation:
\[
142^\circ + m\angle UXS = 180^\circ
\]

Step3: Solve for \( m\angle UXS \)

Subtract \( 142^\circ \) from both sides:
\[
m\angle UXS = 180^\circ - 142^\circ = 38^\circ
\]

Answer:

\( 38 \)