It is often possible to find a missing angle when given some of the
angles of a quadrilateral.
It is important to remember that
the sum of the
angles of any quadrilateral is 360º.
The two acute angles of a
parallelogram are each 45º.
What is the angle measure of each obtuse angle?
If the
sum of the angles of the parallelogram is 360º, and the sum of
the two acute angles is 90º, we have 270º left between the two
obtuse angles. When we divide the 270º between the two
obtuse angles, each angle's measure is 135º. 
The two obtuse angles of this
trapezoid are each 117º.
What is the angle measure of each acute angle?
The
sum of the angles of the trapezoid is 360º. The sum of
the two obtuse angles is 234º, leaving 126º between the two
acute angles. 126º divided by 2 equals 63º for each
acute angle. 
In this trapezium, the two
acute angles have measures of 35º
and 70º. If one obtuse angle measures 145º, what is the
angle measure of the second obtuse angle?
The
sum of the angles of the trapezium is 360º. The sum of
the three given angles is 250º. This leaves 110º for the
fourth angle measure. 
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