Question
Find the value of c in rhombus UVWX.
W
V
U
X
c
3c–60°
c=
°
W
V
U
X
c
3c–60°
c=
°
Answers
GPT-4o mini
In a rhombus, the opposite angles are equal, and adjacent angles are supplementary. Given the angles in rhombus UVWX being \( c \) and \( 3c - 60^\circ \), we can use these properties to find the value of \( c \).
Since adjacent angles in a rhombus are supplementary, we can set up the following equation:
\[
c + (3c - 60^\circ) = 180^\circ
\]
Simplifying this equation:
\[
c + 3c - 60^\circ = 180^\circ
\]
\[
4c - 60^\circ = 180^\circ
\]
\[
4c = 180^\circ + 60^\circ
\]
\[
4c = 240^\circ
\]
\[
c = \frac{240^\circ}{4}
\]
\[
c = 60^\circ
\]
Thus, the value of \( c \) is \( 60^\circ \).
Since adjacent angles in a rhombus are supplementary, we can set up the following equation:
\[
c + (3c - 60^\circ) = 180^\circ
\]
Simplifying this equation:
\[
c + 3c - 60^\circ = 180^\circ
\]
\[
4c - 60^\circ = 180^\circ
\]
\[
4c = 180^\circ + 60^\circ
\]
\[
4c = 240^\circ
\]
\[
c = \frac{240^\circ}{4}
\]
\[
c = 60^\circ
\]
Thus, the value of \( c \) is \( 60^\circ \).