Answer:
x = 10
y = 5
Angle 1: 80 degrees
Angle 2: 45 degrees
Angle 3: 100 degrees
Angle 4: 35 degrees
Angle 5: 35 degrees
Angle 6: 45 degrees
Angle 7: 100 degrees
Step-by-step explanation:
Since we know angle 1 is equal to 80, we can say that angle 7 is 100, since a line makes 180 degrees. Because of the congruence statements, we can assume angle 3 is also 100 degrees. That means, that out of the 360 degrees that make up a 4 sided shape, we are left with 160. Those 160 are shared with angles 2,4,5 and 6.
To find these, we need to find 5 and 6. But we need to find x before we can solve for those. So take the equations from 5 and 6 to solve for x.
(3x+5)+(5x-5)+100=180
(3x+5)+(5x-5)=80
8x=80
x=10
Now plug x in to solve for angle 5 and 6
3(10)+5 = 35. Angle 5
5(10)-5 = 45. Angle 6
Now, because we know that there are only 160 degrees left to share between angles 2,4,5,6 we can say that angles 2+5=80 and 4+6=80. We already figures out what angle 5 and 6 are, so just substitute and solve.
(angle 2)+35 = 80
(angle 2) = 45 degrees
(angle 4)+45 = 80
(angle 4) = 35 degrees
To solve for y, set angle 7 equal to 100 degrees:
100 = y^2 + 15y
100 = y(y+15)
y = 5
