Answer:
7. 42 degrees
8. 58 degrees
Step-by-step explanation:
Question 7
The three angles on the bottom line add up to 180.
65 + 31 + 2y = 180
2y = 84
So y = 42
Question 8
Let's start with the triangle with the 27 degree angle.
We have 27 + 90 + z = 180 (z is the top right angle)
z = 63 (which is also the bottom left angle of the triangle with the 32 degree angle).
63 + 32 + x = 180
x = 85 degrees
Now we look at the bottom polygon with the y degree angle we're trying to find.
We have one angle opposite x and another opposite z.
The angle opposite x + x = 180
The angle opposite x + 85 = 180
The angle opposite x = 95
The angle opposite z + z = 180
The angle opposite z + 63 = 180
The angle opposite z = 117
The sum of the interior angles of a polygon equals the number of sides less 2 * 180. We have four sides, so the interior angles add up to 360.
90 + 95 + 117 + y = 360
Therefore y = 58 degrees
