Question
Find the value of s in rhombus GHIJ.
H
I
J
G
3s+50°
8s–50°
s=
°
H
I
J
G
3s+50°
8s–50°
s=
°
Answers
GPT-4o mini
In a rhombus, the opposite angles are equal, and its adjacent angles are supplementary. Therefore, we can set up an equation using the angle measures provided based on the properties of a rhombus.
Given:
1. One angle \( H = 3s + 50^\circ \)
2. The adjacent angle \( G = 8s - 50^\circ \)
Since the two angles in a rhombus are supplementary, we have:
\[
(3s + 50) + (8s - 50) = 180
\]
Now simplify the equation:
\[
3s + 50 + 8s - 50 = 180
\]
\[
11s = 180
\]
Now solve for \( s \):
\[
s = \frac{180}{11}
\]
Now, we calculate \( s \):
\[
s \approx 16.36^\circ
\]
So the value of \( s \) in degrees is approximately \( 16.36 \) or you can keep it as \( \frac{180}{11} \).
Given:
1. One angle \( H = 3s + 50^\circ \)
2. The adjacent angle \( G = 8s - 50^\circ \)
Since the two angles in a rhombus are supplementary, we have:
\[
(3s + 50) + (8s - 50) = 180
\]
Now simplify the equation:
\[
3s + 50 + 8s - 50 = 180
\]
\[
11s = 180
\]
Now solve for \( s \):
\[
s = \frac{180}{11}
\]
Now, we calculate \( s \):
\[
s \approx 16.36^\circ
\]
So the value of \( s \) in degrees is approximately \( 16.36 \) or you can keep it as \( \frac{180}{11} \).