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

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~~