Question

1. find $m\angle rtv$. consecutive=180

$(6x + 1)^\circ$
$(x + 4)^\circ$

Explanation:

Step1: Identify alternate interior angles

Since $SU \parallel RT$ and $ST$ is a transversal, $\angle STU = \angle RTV = (x+4)^\circ$, and $\angle SVU$ and $\angle RTV$ are same-side interior angles, so they are supplementary:
$$(6x+1) + (x+4) = 180$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$:
$$7x + 5 = 180$$
$$7x = 175$$
$$x = \frac{175}{7} = 25$$

Step3: Calculate $m\angle RTV$

Substitute $x=25$ into $(x+4)^\circ$:
$$m\angle RTV = 25 + 4 = 29$$

Answer:

$29^\circ$