Calculate the measures of the unmarked angles of the parallelogram if x = 5 units.
Hint
Would the measures of the angles be different if x = 500 units?
Answer
70°, 70°, and 110°
Example 2
If the one angle of a parallelogram measures 40°, find the measures of the other three angles.
Hint
What do we know about the angles of parallelograms—or quadrilaterals in general?
Answer
40°, 140°, and 140°
Example 3
In quadrilateral ABCD, ∠1 is not congruent to ∠3. Prove ABCD is not a parallelogram.
Hint
When you see a not in the conclusion, it's a pretty good indicator to use an indirect proof.
Answer
Let's assume ABCD is a parallelogram (by contradiction). If that assumption were true, then we know that opposite angles (like ∠1 and ∠3) would be congruent. Since we're given that ∠1 ≇ ∠3, this contradicts with our assumption. As such, we know that ABCD is not a parallelogram.
Example 4
Calculate the perimeter of the parallelogram FGHJ shown in the figure.
Hint
There's a rumor going around that opposite sides of a parallelogram are congruent. But shhhhh. You didn't hear it from us.
Answer
36 units
Example 5
Calculate the perimeter of the parallelogram if the length of the horizontal side is 12.
Hint
Use the Pythagorean Theorem, young grasshopper. It will bring you many good fortunes (and among them, the right answer).
Answer
34 units
Example 6
Calculate the perimeter of the parallelogram.
Hint
Either use your special triangle knowledge or make use of some trig ratios. Your choice.
