Answer for Problem #1:
- Yes you can determine that this quadrilateral is a parallelogram because opposite side are congruent, opposite angles are congruent, and opposite sides are parallel.
Answer for Problem #2:
Plug in A=16(12)
A=192
- Area of a parallelogram=b(h), where b is base and h is height.
Plug in A=16(12)
A=192
- The area of Mark's garden will be 192 square yards.
Answer for Problem #3:
2x=180+56
2x=236
x=118
- Let "x" be the angle measure in degrees of the first two given angles. Then the angle of the second angle is x-56 in accordance with the parallelogram condition. x+(x-56)=180.
- Since the given two angles of the parallelogram are not congruent, they are not opposite. So, they are consecutive.
2x=180+56
2x=236
x=118
- So the first angle measure is 118 degrees. Then the two consecutive angles are 180-118=62. You can check that the first angle is in 56 degrees greater than the consecutive, as it is stated by the condition: 118-62=56.
The angles of the parallelogram are 118 °, 62 °, 118 °, 62 ° - To check, add all angles. 118+62+118+62=360