Answer:
4. 94 degrees
5. 60 degrees
Step-by-step explanation:
4. This is a pentagon. By definition, all the angles should add up to 540 degrees. So, we can just add up all those expressions and solve for x:
(4x + 2) + 132 + (4x - 10) + (5x - 11) + 128 = 540
Combine like terms:
13x + 241 = 540
Solve for x:
13x = 299
x = 23
Now put this into the expression for angle P:
P = 4x + 2 = 4 * 23 + 2 = 92 + 2 = 94
Thus, P is 94 degrees.
5. Since angles 1, 2, and 3 are equal, then their supplementary angles are also equal. Say that each supplementary angle is x.
We also see that angle 4 = angle 3 + 10. We already set the supplementary of angle 3 as x, so that means that angle 3 = 180 - x (by definition of supplementary angles). This means that angle 4 = 180 - x + 10 = 190 - x. Angle 4's supplementary angle is the one inside the hexagon, and it will be: 180 - (190 - x) = x - 10.
Since angles 4 and 5 are equal, then their supplementary angles are equal, as well. So, the supplementary angle of angle 5 is x - 10.
Finally, we see that the last angle left to figure out in the hexagon is the one with the square. That is 90 degrees (by definition).
The sum of the angles in a hexagon, by definition, is 720. So, let's write all these expressions and set them equal to 720:
x + x + x + (x - 10) + (x - 10) + 90 = 720
Combine like terms:
5x + 70 = 720
Solve for x:
5x = 650
x = 130
The supplementary angle of angle 5 is x - 10 = 130 - 10 = 120. So, the measure of angle 5 is 180 - 120 = 60.
Hope this helps!
