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Question

An illustration shows three rays passing through three points from a common origin point at upper B. Point upper C is to the horizontal left of upper B. A ray from upper B joins upper C with an arrow near upper C. Point upper D is on the top inclined slightly to the right of point upper B. A ray from upper B joins upper D with an arrow near upper D. Point upper A is to top right of point upper B. A ray from upper B joins upper A with an arrow near upper A. Angle upper C upper B upper A is labeled as 155 degrees. Angle upper D upper B upper A is labeled as 60 degrees.

The measure of ∠ABD is 60° and the measure of ∠ABC is 155° . What is the measure of ∠DBC ?

(1 point)
Responses

215°
215 degrees

155°
155 degrees

180°
180 degrees

95°
95 degrees
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Answer 1

To find the measure of ∠DBC, we can use the fact that the sum of the angles in a triangle is 180 degrees.

∠ABC + ∠BCA + ∠CAB = 180

Plugging in the given measures:

155° + ∠BCA + 60° = 180°

Adding the like terms:

∠BCA + 215° = 180°

Subtracting 215° from both sides:

∠BCA = 180° - 215°

Simplifying:

∠BCA = -35°

Since the measure of an angle cannot be negative, we can conclude that there is an error in the given information or the illustration. Therefore, none of the provided answer choices are correct.