Use the image to answer the question.

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

180°
180 degrees

155°

95

Answer 1

To find the measure of ∠DBC, we can use the information given about the angles around point B.

The angle ∠ABC is 155°, and we know the angle ∠ABD is 60°. To find the measure of ∠DBC, we can use the fact that the sum of the angles around point B must equal 360°.

The angles around point B are ∠ABC, ∠ABD, and ∠DBC. Therefore, we can write the equation:

∠ABC + ∠ABD + ∠DBC = 360°

Plugging in the values we have:

155° + 60° + ∠DBC = 360°

Now, simplify the equation:

215° + ∠DBC = 360°

Subtract 215° from both sides:

∠DBC = 360° - 215°

∠DBC = 145°

Therefore, the answer is not listed in the options provided. The most accurate conclusion would be that the measure of ∠DBC is 145°.