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

m∠DAC = 29°

Explanation:

Step 1: Draw it.

See attached picture. In the picture I also drew two orange angles that are congruent. They are congruent because line segments DC and AB are parallel and they are alternate interior angles.

Step 2: Find the angle.

Notice the two congruent orange angles in the picture. They are congruent because they are alternate interior angles.

The angle ADC, which measures 127°, forms a straight angle (180°) with the orange angle. They are supplementary angles.

orange angle + m∠DAC = 180°

orange angle + 127° = 180°

orange angle = 53°

Angle DAB is one of the orange angles. We can see that it consists of two other angles - angle CAB (24°) and angle DAC (x). We calculated that the two angles together measure 53°.

m∠DAC + m∠ CAB = orange angle

m∠DAC + m∠ CAB = 53°

m∠DAC + 24° = 53°

m∠DAC = 29°