Final answer:
The measure of angle ABD in a triangle, given that angles BAC and BCD are 33 and 35 degrees respectively, is found to be 79 degrees.
Step-by-step explanation:
The question revolves around the properties of triangles and angle measures. Given two angles in a triangle, the measure of the third angle can be found by using the fact that the sum of all interior angles in a triangle is always 180 degrees. Assuming there's a typo in the question and it's referring to triangle ABC and angle BCD, having known angle BAC as 33 degrees and angle BDC as 35 degrees, if ABC and BCD share a common vertex and arm, angle ABC would be made up of angle BAC and angle BDC; therefore, angle ABD would be the remaining angle in triangle ABC. Since the sum of angles BAC, ABC, and ACB is 180 degrees, we calculate angle ABD by subtracting the known angles from 180.
If we assume that angle ABC is simply angle BAC plus angle BDC, then:
- Angle ABC = angle BAC + angle BDC
- Angle ABC = 33 degrees + 35 degrees
- Angle ABC = 68 degrees
To find angle ABD:
- Sum of angles in triangle ABC = 180 degrees
- Angle ABD = 180 degrees - angle BAC - angle ABC
- Angle ABD = 180 degrees - 33 degrees - 68 degrees
- Angle ABD = 79 degrees
This calculation reveals that angle ABD has a measure of 79 degrees.