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

155°
155 degrees

95°
95 degrees

215°
215 degrees

180°

Answer 1

To find the measure of ∠DBC, we can use the fact that the sum of the angles around point B must equal 360 degrees.

We already have:

• ∠ABD = 60°
• ∠ABC = 155°

Now, we can calculate ∠DBC:

\[ \text{Angle around point B} = \angle ABC + \angle ABD + \angle DBC = 360° \] \[ \angle DBC = 360° - (\angle ABC + \angle ABD) \] \[ \angle DBC = 360° - (155° + 60°) \] \[ \angle DBC = 360° - 215° \] \[ \angle DBC = 145° \]

However, since angles can also be described in terms of negative measurements or can be seen in a different direction, and knowing that 360° - 145° would give the same angle coming in the other direction around B (215°), we confirm that the measure of ∠DBC can be expressed as:

\[ \angle DBC = 215° \]

Thus, the measure of ∠DBC is:

• 215°