The unknown side lengths are
Large triangle 10
Medium triangle 2
Small triangle 12/5 or 2.4
Step-by-step explanation:
EFD to ABC is 0.4 or 2/5
EFD to GHI is 0.24 or 6/25
ABC to GHI is 0.6 or 6/10
The opposite angles of a parallelogram are equal.
Therefore
m∠A = m∠C, so that
5y - 3 = 3y + 27
Subtract 3y from each side.
5y - 3y - 3 = 3y - 3y + 27
2y - 3 = 27
Add 3 to each side.
2y - 3 + 3 = 27 + 3
2y = 30
y = 30/2 = 15
Therefore
m∠A = 5*15 - 3 = 72°
m∠C = 72°
Let x = m∠B
Then x = , m∠B = m∠C
Because the sum of the angles in the parallelogram is 360°, therefore
x + x + 72 + 72 = 360
2x = 360-144 = 216
x = 216/2 = 108
Answer:
m∠A = 72°
m∠B = 108°
The first set:
3x + 2y = 2 ---1)
5x + 4y = 6 ---2)
From 1), multiply all by 2, 6x + 4y = 4 ---3)
3) - 2),
6x + 4y - (5x + 4y) = 6 - 4
6x + 4y - 5x - 4y = 2
x = 2
Sub in x = 2 into 1),
3(2) + 2y = 2
2y = -4
y = -2
(2 , -2)
The second set:
3x + 2y = 2 ---1)
11x + 8y = 10 ---2)
From 1), multiply all by 4, 12x + 8y = 8 ---3)
3) - 2),
12x + 8y - (11x + 8y) = 8 - 10
12x + 8y - 11x - 8y = -2
x = -2
From this x value alone, we can tell that these two linear systems do NOT have the same solution as they meet at different coordinates.
Hope this helped! Ask me if there's any working from here that you don't understand! :)