Final answer:
Angle DEC measures 60°, calculated by subtracting the sum of the given angles (BAC and CBA) from the total sum of angles in a triangle, which is 180°. The correct answer is 3.
Step-by-step explanation:
To find the measure of angle DEC, we need to use the fact that the sum of the angles in a triangle is 180°. Given that the measure of angle BAC is 50° and the measure of angle CBA is 70°, we can determine the measure of angle ACB as follows:
Sum of angles in triangle ABC = angle BAC + angle CBA + angle ACB = 180°.
50° (angle BAC) + 70° (angle CBA) + angle ACB = 180°.
120° (sum of given angles) + angle ACB = 180°.
We subtract 120° from 180° to find angle ACB.
Angle ACB = 180° - 120° = 60°.
Therefore, if angle DEC is also angle ACB or corresponds to the same internal angle, then the measure of angle DEC is also 60°. The correct answer is option 3.