Question

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?

Answer 1

Answer:

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Answer 2

Answer:

$m\angle DAC=29^{\circ}$

Step-by-step explanation:

We are given that ABCD is a parallelogram with diagonal AC.

$m\angle CAB=24^{\circ}$

$m\angle ADC=127^{\circ}$

We have to find the measure of angle DAC.

$AB\parallel CD,BC\parallel AD$

$m\angle CAB=m\angle ACD=24^{\circ}$ (Alternate interior angle theorem)

In triangle ACD

$m\angle ACD+m\angle ADC+m\angle DAC=180^{\circ}$

(Triangle angles sum property)

Substitute the values then we get

$24+127+m\angle DAC=180$

$m\angle DAC+151=180$

$m\angle DAC=180-151=29^{\circ}$