Answer:
25. D 27. D 28. A 29. D. x = 7, y = 26 31. D. 120 degrees
Step-by-step explanation:
25. Since the two parallelograms are congruent, you know what ∠B and ∠Y are supplementary.
This means that 3m + 70 + 80 = 180
3m + 150 = 180
3m = 30
D. m = 10
27. Since a vertex is (2,0), you know that two other vertexes are five units away in one direct and the other vertex will be five up or down and five over.
A is 5 units over, and that's a possible other coordinate, so it can't be A.
B is 5 over, so it's a possibility and it can't be B.
C is down 5 and 5 over, so it can be the coordinate across from (2,0), so it can't be C.
D is 7 up and 2 over, which isn't within our 5 unit frame! So it must be D!
E is 5 up and 5 over, so it can still count as a possibility.
28. When you observe the coordinates, you'll notice that FG ║ HI, and FH ║ GI. This eliminates the possibility of it being a kite and ensures that it will at least be a parallelogram!
From here, you can also observe that FG ≅ HI, and FH ≅ GI. This shows you that it's not a square despite that it has right angles.
The presence of right angles shows that it's not a rhombus and instead must be a rectangle.
29. Even though the problem only identifies it as a quadrilateral, it must be a parallelogram because of the parallel sides. Opposite angles on parallelograms are congruent, so we can begin with:
6x - 8 = 4x + 6
2x = 14
x = 7
From here, you can plug "x" back into the equation to find the value of those two angles.
6(7) - 8
42 - 8
34
Now that we know that those two angles are 34 degrees, we know that they total to 68 degrees.
Since the sum of internal angles on a quadrilateral is 360 degrees, the other two anglers must be 360 - 68.
That means the total of those two angles is 292 degrees.
Since we know the angles are equal (def. of parallelogram), we know that:
146 = 5y + 16
140 = 5y
y = 26
D. x = 7, y = 26
31. The arc is 120 degrees because the angle because at the other side instead of at the center of the circle, so you double the angle.
is the center
is the radius