Question

find the measure of ∠tus. m∠tus =

Explanation:

Step1: Identify angle - relationship

Since $\angle TUS$ and the angle $(63 - 3x)^{\circ}$ are vertical angles, they are equal. Also, $\angle TUS$ and $(55 - x)^{\circ}$ are corresponding angles (assuming $PQ\parallel RS$), so $55 - x=63 - 3x$.

Step2: Solve for $x$

Add $3x$ to both sides of the equation $55 - x=63 - 3x$:
$55 - x+3x=63 - 3x+3x$, which simplifies to $55 + 2x=63$.
Subtract 55 from both sides: $2x=63 - 55$, so $2x = 8$.
Divide both sides by 2: $x = 4$.

Step3: Find $\angle TUS$

Substitute $x = 4$ into the expression for $\angle TUS$ (using $63 - 3x$).
$\angle TUS=63-3\times4$.
$=63 - 12$.
$=51^{\circ}$.

Answer:

$51$