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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?

Respuesta :

slysoph
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~~

The diagonal AC can be considered a transversal to the CD and AB of tht parallelogram ABCD

The measure of ∠DAC is 34°

Reason:

The given parameters;

ABCD is a parallelogram; Given

AC is a diagonal of parallelogram ABCD; Given

m∠CAB = 21°, and m∠ADC = 125°; Given

We have;

m∠CAB ≅ m∠ACD by alternate interior angles theorem

∴ m∠CAB = m∠ACD = 21°

m∠ACD + m∠ADC + m∠DAC = 180°

m∠DAC = 180° - (m∠ACD + m∠ADC)

∴ m∠DAC = 180° - (21° + 125°) = 34°

The measure of ∠DAC = 34°

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