The measure of ∠ABD is 60° and the measure of ∠ABC is 155° . What is the measure of ∠DBC ?
(1 point)
Responses
155°
155 degrees
180°
180 degrees
95°
95 degrees
215°
To find the measure of ∠DBC, we can use the fact that the sum of the angles in a triangle is 180°. Since we know the measures of ∠ABD and ∠ABC, we can subtract those from 180° to find the measure of ∠DBC:
∠DBC = 180° - ∠ABD - ∠ABC
∠DBC = 180° - 60° - 155°
∠DBC = 180° - 215°
∠DBC = -35°
However, angles cannot have negative measure, so the measure of ∠DBC cannot be -35°.
Therefore, none of the given responses (155°, 180°, 95°, 215°) are correct.
pick one
I apologize for the confusion in my previous response. Since ∠DBC cannot have a negative measure, we should consider the angle to be an exterior angle to the triangle.
By using the exterior angle theorem, we can determine that the measure of ∠DBC is equal to the sum of the measures of ∠ABD and ∠ABC.
∠DBC = ∠ABD + ∠ABC
∠DBC = 60° + 155°
∠DBC = 215°
Therefore, the correct measure of ∠DBC is 215°.