Question

5 fill in the blank 12 points line rs and vw are parallel. find the measure of the angles in the triangle rts and vtw. the measure of rts type your answer... the measure of tsr type your answer... the measure of vwt type your answer... the measure of wtv type your answer...

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle vertical to the given $79^{\circ}$ angle has the same measure. So, $\angle RTS = 79^{\circ}$.

Step2: Use corresponding - angle property

Since $RS\parallel VW$, the angle corresponding to the $33^{\circ}$ angle has the same measure. In $\triangle RTS$, $\angle TSR = 33^{\circ}$.

Step3: Use angle - sum property of a triangle

In $\triangle RTS$, the sum of interior angles of a triangle is $180^{\circ}$. Let $\angle TRS = x$. Then $x+79^{\circ}+33^{\circ}=180^{\circ}$, so $x = 180^{\circ}-(79^{\circ}+33^{\circ})=68^{\circ}$. $\angle VW T$ and $\angle TRS$ are corresponding angles, so $\angle VW T=68^{\circ}$.

Step4: Use vertical - angle property for $\angle WTV$

$\angle WTV$ and $\angle RTS$ are vertical angles. So $\angle WTV = 79^{\circ}$.

Answer:

The measure of $RTS$: $79^{\circ}$
The measure of $TSR$: $33^{\circ}$
The measure of $VWT$: $68^{\circ}$
The measure of $WTV$: $79^{\circ}$