Answer:
m∠DAC = 29°
Step-by-step 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°
