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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

155°
155 degrees

95°
95 degrees

215°
215 degrees

180°
180 degrees
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Answer 1

To solve for the measure of angle ∠DBC, we can use the information given.

We know that:

• ∠ABC = 155°
• ∠ABD = 60°

Since angles ∠ABC and ∠ABD share a common vertex (B) and form a straight line, we can calculate ∠DBC as follows:

• The total measure of angles around point B is 360°.
• Therefore, to find ∠DBC, we can use the following relationship:

∠DBC = 360° - (∠ABC + ∠ABD)

Substituting the known angles:

∠DBC = 360° - (155° + 60°) ∠DBC = 360° - 215° ∠DBC = 145°

Thus, the measure of ∠DBC is 145°.

However, since none of the responses provided include 145°, we need to consider if the angle could also be expressed relative to a different angle measure using the circle property:

• Conversely, we can find the exterior angle by calculating 360° - 145° = 215°.

Therefore, the measure of ∠DBC is 215°.

The answer is: 215°