figure tuvs is a parallelogram. which angles equal 91°? angles t and v angles s and u angles u and v angles…

Explanation:

Step1: Recall property of parallelogram

In a parallelogram, opposite - angles are equal. So, $\angle U=\angle S$ and $\angle T=\angle V$, and adjacent - angles are supplementary ($\angle T+\angle U = 180^{\circ}$, $\angle U+\angle V = 180^{\circ}$, $\angle V+\angle S = 180^{\circ}$, $\angle S+\angle T = 180^{\circ}$). Also, $\angle U=(4x + 9)^{\circ}$ and $\angle S=(6x - 29)^{\circ}$. Since $\angle U=\angle S$, we set up the equation $4x + 9=6x - 29$.

Step2: Solve the equation for x

Subtract $4x$ from both sides: $9 = 6x-4x - 29$. So, $9 = 2x-29$. Add 29 to both sides: $9 + 29=2x$, which gives $38 = 2x$. Divide both sides by 2: $x = 19$.

Step3: Find the measure of $\angle U$ and $\angle S$

Substitute $x = 19$ into the expression for $\angle U$: $\angle U=4x + 9=4\times19+9=76 + 9=85^{\circ}$. Substitute $x = 19$ into the expression for $\angle S$: $\angle S=6x - 29=6\times19-29=114 - 29=85^{\circ}$.

Step4: Find the measure of $\angle T$ and $\angle V$

Since $\angle T+\angle U = 180^{\circ}$ and $\angle U = 85^{\circ}$, then $\angle T=180 - 85=95^{\circ}$. Since $\angle T=\angle V$, $\angle V = 95^{\circ}$. However, if we assume the non - adjacent angles are equal (a wrong assumption for a general parallelogram but let's check the options). In a parallelogram, opposite angles are equal. If we assume the question is about non - adjacent equal angles. We know that in a parallelogram, opposite angles are equal. Let's assume we want to find which pair of angles can be equal to $91^{\circ}$. Since opposite angles are equal in a parallelogram, angles $S$ and $U$ are opposite angles and angles $T$ and $V$ are opposite angles. If we assume $\angle U=\angle S = 91^{\circ}$ (because opposite angles of a parallelogram are equal).

Answer:

angles S and U