Question
Find the value of v in rhombus ABCD.
A
D
C
B
3v–32°
6v–40°
v=
°
A
D
C
B
3v–32°
6v–40°
v=
°
Answers
GPT-4o mini
In a rhombus, opposite angles are equal, and adjacent angles are supplementary (they add up to 180 degrees).
Given the angles \(3v - 32^\circ\) and \(6v - 40^\circ\) are adjacent angles, we can set up the following equation:
\[
(3v - 32) + (6v - 40) = 180
\]
Now, combine like terms:
\[
3v - 32 + 6v - 40 = 180
\]
\[
9v - 72 = 180
\]
Next, add 72 to both sides:
\[
9v = 252
\]
Now, divide by 9:
\[
v = \frac{252}{9} = 28
\]
Thus, the value of \(v\) is:
\[
\boxed{28^\circ}
\]
Given the angles \(3v - 32^\circ\) and \(6v - 40^\circ\) are adjacent angles, we can set up the following equation:
\[
(3v - 32) + (6v - 40) = 180
\]
Now, combine like terms:
\[
3v - 32 + 6v - 40 = 180
\]
\[
9v - 72 = 180
\]
Next, add 72 to both sides:
\[
9v = 252
\]
Now, divide by 9:
\[
v = \frac{252}{9} = 28
\]
Thus, the value of \(v\) is:
\[
\boxed{28^\circ}
\]