Question
Find the value of v in rhombus FGHI.
H
I
F
G
3v–55°
3v–95°
v=
°
H
I
F
G
3v–55°
3v–95°
v=
°
Answers
GPT-4o mini
In a rhombus, opposite angles are equal, and the adjacent angles are supplementary (they add up to 180°). Therefore, if we are given two angles of the rhombus as \( 3v - 55° \) and \( 3v - 95° \), we can set up the following equation, because these two angles are adjacent:
\[
(3v - 55) + (3v - 95) = 180
\]
Now, let's simplify that equation:
1. Combine like terms:
\[
3v - 55 + 3v - 95 = 180
\]
\[
6v - 150 = 180
\]
2. Now, add 150 to both sides:
\[
6v = 330
\]
3. Divide both sides by 6:
\[
v = 55
\]
Thus, the value of \( v \) is \( 55° \).
\[
(3v - 55) + (3v - 95) = 180
\]
Now, let's simplify that equation:
1. Combine like terms:
\[
3v - 55 + 3v - 95 = 180
\]
\[
6v - 150 = 180
\]
2. Now, add 150 to both sides:
\[
6v = 330
\]
3. Divide both sides by 6:
\[
v = 55
\]
Thus, the value of \( v \) is \( 55° \).