Question

find the measure of ∠tus.
m∠tus = □°

Explanation:

Step1: Identify angle - relationship

Since $\angle TUS$ and the angle $(55 - x)^{\circ}$ are corresponding angles (assuming $PQ\parallel RS$), they are equal. Also, vertical - angles are equal. We can set up an equation using the fact that the angles $(55 - x)^{\circ}$ and $(63 - 3x)^{\circ}$ are related. If the lines $PQ$ and $RS$ are parallel, then $(55 - x)=(63 - 3x)$ (corresponding angles).

Step2: Solve the equation for $x$

\[

$$\begin{align*} 55 - x&=63 - 3x\\ 3x - x&=63 - 55\\ 2x&=8\\ x& = 4 \end{align*}$$

\]

Step3: Find the measure of $\angle TUS$

Substitute $x = 4$ into the expression for $\angle TUS=(55 - x)^{\circ}$.
\[

$$\begin{align*} m\angle TUS&=55-4\\ &=51^{\circ} \end{align*}$$

\]

Answer:

$51$