Question

if m∠sxt = 142°, then what is m∠uxs?

Explanation:

Step1: Identify vertical - angles

$\angle SXT$ and $\angle 3$ are vertical - angles. So, $m\angle 3=m\angle SXT = 142^{\circ}$.

Step2: Use linear - pair property

$\angle 3$ and $\angle UXS$ form a linear pair. Since the sum of angles in a linear pair is $180^{\circ}$, if we let $m\angle UXS=x$, then $x + m\angle 3=180^{\circ}$.

Step3: Solve for $m\angle UXS$

$m\angle UXS=180^{\circ}-m\angle 3$. Substitute $m\angle 3 = 142^{\circ}$ into the equation. So, $m\angle UXS=180 - 142=38^{\circ}$.

Answer:

$38^{\circ}$