Answer: x = 114
Step-by-step explanation:
Angle A is equivalent to angle D because of the properties of parallelograms. So we know angle A is 66 degrees. Angles C and B also have the same measure because they are opposite angles. The sum of all four angle measures is 360 degrees.
Therefore, you can write this equation:
m<A + m<B + m<C + m<D = 360
Step 1) plug in the degree measure of each angle that you know.
(I will represent angle C with “x”)
66 + m<B + x + 66 = 360
(We know that the m<B is the same as m<C, so we can plug in “x” for m<B)
66 + x + x + 66 = 360
(x + x is the same as 2x)
66 + 2x + 66 = 360
(66 + 66 = 132)
132 + 2x = 360
Step 2) solve for x by continuing with this equation: 132 + 2x = 360
(Subtract 132 from both sides)
2x = 228
(Divide by 2 on both sides)
x = 228/2
(228/2 equals 114)
x = 114
Check:
Add all four angle measures. It should add up to 360.
66 + 114 + 114 + 66
180 + 114 + 66
294 + 66
360
Yay it worked!
FYI: the angles that are across from each other in a parallelogram are always congruent. The sides that are opposite (across from) each other are also congruent. All 4 angles in a parallelogram will add up to 360 degrees. This info will help when you’re solving for the sides or angles of a parallelogram. Good luck!
