The sum of the two angles of a parallelogram is 140 °. Find the degree measures of all angles of the parallelogram.

The order of solving this problem is as follows:
we build a drawing – this will be a parallelogram ABCD (AB // CD, BC // AD);
find out the sum of which angles is 140 degrees;
we find the degree measures of all angles.
By the property of a parallelogram, 2 angles adjacent to the same side always add up to 180 degrees. This can be seen if you extend one of the parties, for example AD. Angles with equal measures are indicated by the same numbers.
Then we are talking about opposite angles, and acute ones, since two obtuse angles in total will always be greater than 180 degrees:
angle BAD + angle BСD = 140 degrees.
By the property of a parallelogram, the opposite angles are equal, which means
angle BAD = angle BСD = 140/2 = 70 degrees.
angle ABC = angle ADC = 180 – 70 = 110 degrees (by the property of internal one-sided corners).



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