Final answer:
To find the measure of ∡bac, we find that an error might be present due to the sum of the angles given being more than 180°. If ∡bcd is an exterior angle, applying the exterior angle theorem gives us ∡bac = 35°.
Step-by-step explanation:
The student has asked about finding the measure of the angle ∡bac when given the measures of ∡bcd, which is 120°, and ∡abc, which is 85°. To find the measure of ∡bac, we need to remember that the sum of the angles in a triangle equals 180°. We have:
- ∡abc + ∡bac + ∡bca = 180°
- 85° + ∡bac + 120° = 180°
- ∡bac = 180° - 85° - 120°
- ∡bac = -(25°)
However, since an angle cannot have a negative degree, there might be a typo in the provided measures. If the student meant the angle outside the triangle, then the exterior angle theorem applies, which states that the exterior angle is equal to the sum of the two opposite interior angles. If ∡bcd is the exterior angle, then:
- ∡bac + ∡abc = ∡bcd
- ∡bac = ∡bcd - ∡abc
- ∡bac = 120° - 85°
- ∡bac = 35°
In this case, ∡bac would measure 35°.