Question

What is m∠SVT?



Enter your answer in the box.


In the image we are vertical angles

angles SVT is (5y + 9) degress
angles RVU is (8y - 33) degress

Answer 1

Since angles SVT and RVU are vertical angles, they are equal to each other. Thus, you can set up the equation:

\[
5y + 9 = 8y - 33
\]

Now, solve for \(y\):

1. Subtract \(5y\) from both sides:
\[
9 = 3y - 33
\]

2. Add \(33\) to both sides:
\[
42 = 3y
\]

3. Divide by \(3\):
\[
y = 14
\]

Now, substitute \(y = 14\) back into the expression for angle SVT:

\[
m∠SVT = 5y + 9
\]
\[
m∠SVT = 5(14) + 9
\]
\[
m∠SVT = 70 + 9
\]
\[
m∠SVT = 79
\]

Thus, the measure of angle SVT is:

\[
\boxed{79}
\] degrees.