ABCD is a parallelogram with diagonal AC. If the measure of angle CAB is 24° and the measure of angle ADC is 127°, what is the measure of angle DAC? Parallelogram ABCD with diagonal AC; the measure of angle ADC is 127 degrees, and the measure of angle CAB is 24 degrees. 29° 48° 79° 103°

A). 29°

Explanation:

Given that,

∠ADC = 127°

In case the quadrilateral is a ║gm, the successive angles would be supplementary

∠ADC + ∠ DCB = 180°

By putting the value of ∠ADC, we get

127° + ∠DCB = 180°

 ∵ ∠ DCB = 180° - 127°

∠ DCB = 53°

Because opposite angles of ║gm are ≅. It can be written as;

∠ CAB + ∠ DAC = ∠DCB

by putting the values. We get

24° +  ∠DAC = 53°

 ∠ DAC = 53° - 24°

∵ ∠DAC = 29°

Therefore, the measure of ∠DAC is 29°.

Thus, option A is the correct answer.

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