Question

find the measure of ∠tus. m∠tus = \boxed{}^circ (diagram shows parallel lines pq, rs with transversal no; ∠at t: (55 - x)°, ∠at u: (63 - 3x)°)

Explanation:

Step1: Identify parallel lines and transversal

Lines \( pQ \) and \( RS \) are parallel, and \( NO \) is a transversal. So, \( \angle TUS \) and \( \angle NTQ \) are alternate interior angles, hence equal. So, \( 63 - 3x = 55 - x \).

Step2: Solve for \( x \)

\[

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

\]

Step3: Find \( m\angle TUS \)

Substitute \( x = 4 \) into \( 63 - 3x \):
\[

$$\begin{align*} 63 - 3(4) &= 63 - 12\\ &= 51 \end{align*}$$

\]

Answer:

\( 51 \)