what is the measure of angle trv? (2x + 10)° (x - 10)° 20° 50° 60° 130°

Explanation:

Step1: Set up equation

Since vertical angles are equal, we have $(2x + 10)=(x - 10)+90$.

Step2: Solve for x

First, expand the right - hand side: $2x+10=x - 10+90$. Then simplify to $2x+10=x + 80$. Subtract x from both sides: $2x - x+10=x - x + 80$, getting $x+10 = 80$. Subtract 10 from both sides: $x=70$.

Step3: Find measure of angle TRV

Substitute $x = 70$ into the expression for angle TRV which is $2x+10$. So, $2\times70+10=140 + 10=150$ (This is wrong above, we should note that $(2x + 10)+(x - 10)=180$ as they are a linear pair). Starting over:

Step1: Set up correct equation

$(2x + 10)+(x - 10)=180$ (linear - pair of angles).

Step2: Solve for x

Combine like terms: $2x+x+10 - 10=180$, so $3x=180$. Divide both sides by 3: $x = 60$.

Step3: Find measure of angle TRV

Substitute $x = 60$ into the expression for angle TRV which is $2x+10$. So, $2\times60+10=120 + 10=130$.

Answer:

$130^{\circ}$