Question

∠T
and ∠R
are vertical angles. m∠T = 3x+36
and ∠R = 6x−9
. What is the measure of ∠T
?(1 point)
Responses

87
87

15
15

81
81

17

Answer 1

Since angles T and R are vertical angles, their measures are equal. Therefore, we can set up the equation:

\[
3x + 36 = 6x - 9
\]

To solve for x, first, rearrange the equation:

\[
36 + 9 = 6x - 3x
\]
\[
45 = 3x
\]

Now, divide both sides by 3:

\[
x = 15
\]

Now that we have the value of x, we can find the measure of angle T:

\[
m∠T = 3x + 36
\]
\[
m∠T = 3(15) + 36
\]
\[
m∠T = 45 + 36
\]
\[
m∠T = 81
\]

Thus, the measure of \(\angle T\) is **81**.