Geometry
Special Quadrilaterals
Name: Sanje Pollard
Date: 4/15/26
Directions: Show all work in the spaces provided as you answer each of the questions that follow.
Part 1: Rectangles
Given that quadrilateral \( F G H I \) is a rectangle, complete each of the following.
1. If \( m \angle 1=3 x-7 \) and \( m \angle 2=x+41 \), then \( x= \) \( \_\_\_\_ \) 14 and \( m \angle 4= \) \( \_\_\_\_ \) \( 55^{\circ} \) .
2. If \( I F=8 y-5 \) and \( G H=3 y+20 \), then
\( y= \) \( \_\_\_\_ \) 5 .
3. If \( m \angle 1=2 x+1 \) and \( m \angle 4=33 \), then \( x= \) \( \_\_\_\_ \) 28 and \( m \angle 3= \) \( \_\_\_\_ \) \( 33^{\circ} \) .
4. If \( I G=8 x-7 \) and \( F H=6 x+31 \), then \( x= \) \( \_\_\_\_ \) 19 .
5. If \( m \angle 3=4 x-12 \) and \( m \angle 4=2 x+10 \), then \( x= \) \( \_\_\_\_ \) 11 \( m \angle 4= \) \( \_\_\_\_ \) \( 32^{\prime} \) and \( m \angle 1= \) \( \_\_\_\_ \) \( 58^{\circ} \) .
6. If \( F G=4 x-3, G H=2 x+1 \), and the perimeter of \( F G H I \) is 80 cm , then \( x= \)
\( \_\_\_\_ \) and \( G H= \) \( \_\_\_\_ \) 15 .
7. If \( F H=9 x-14 \) and \( I R=x+14 \), then \( x= \) \( \_\_\_\_ \) 2 and \( F R= \) \( \_\_\_\_ \) 2 .
8. If \( F G=12 \mathrm{~cm} \), and \( F H=15 \mathrm{~cm} \), then \( G H= \) \( \_\_\_\_ \) 9 cm , and the perimeter of □ FGHI = \( \_\_\_\_ \) 42 cm.