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ABCD is a parallelogram with diagonal AC. If the measure of angle CAB is 21° and the measure of angl...
4 months ago
Q:
ABCD is a parallelogram with diagonal AC. If the measure of angle CAB is 21° and the measure of angle ADC is 125°, what is the measure of angle DAC?
Accepted Solution
A:
Angle DAC is 34 degrees
If a quadrilateral is a parallelogram, consecutive angles are supplementary
Angle ADC + Angle DCB = 180
Substitute the angle measure for ADC
125 + Angle DCB = 180
Subtract 125 from both sides
Angle DCB = 55
Since opposite angles of parallelograms are congruent we can write this equation
Angle CAB + Angle CAD = DCB
Now we substitute the known measures
21 + Angle CAD = 55
Subtract 21 from both sides
Angle CAD = 34
Therefore the measure of angle CAD is 34 degrees
~~hope this helps~~