Question: Find m\angle I in rhombus FGHI.
I
F
G
H
u+53^\circ
3u-93^\circ
m\angle I = ___^\circ
Graph shape: a slanted rhombus labeled F at upper right, G at lower right, H at lower left, and I at upper left; the angle at H is labeled u+53^\circ and the angle at G is labeled 3u-93^\circ; the prompt \u201CFind m\angle I in rhombus FGHI.\u201D is positioned top-left; the answer blank \u201Cm\angle I = ___^\circ\u201D is near bottom-left. position_hint: center
1. **State the problem:** We need to find the measure of angle $m\angle I$ in rhombus $FGHI$ given that $m\angle H = u+53^\circ$ and $m\angle G = 3u-93^\circ$.
2. **Recall properties of a rhombus:** Opposite angles in a rhombus are equal, and adjacent angles are supplementary (sum to $180^\circ$).
3. **Set up equations:** Since $H$ and $G$ are adjacent angles, their measures add up to $180^\circ$:
$$ (u+53) + (3u - 93) = 180 $$
4. **Simplify and solve for $u$:**
$$ u + 53 + 3u - 93 = 180 $$
$$ 4u - 40 = 180 $$
$$ 4u = 180 + 40 $$
$$ 4u = 220 $$
$$ u = \frac{220}{4} $$
$$ u = 55 $$
5. **Find $m\angle H$ and $m\angle G$ using $u=55$:**
$$ m\angle H = u + 53 = 55 + 53 = 108^\circ $$
$$ m\angle G = 3u - 93 = 3(55) - 93 = 165 - 93 = 72^\circ $$
6. **Find $m\angle I$:** Since $I$ is opposite $G$, $m\angle I = m\angle G = 72^\circ$.
**Final answer:**
$$ m\angle I = 72^\circ $$