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 ?

Answer 1

To find the measure of angle \( \angle DBC \), we can use the fact that the angles around point \( B \) must sum to \( 360^\circ \).

We know:

• \( \angle ABC = 155^\circ \)
• \( \angle ABD = 60^\circ \)

We need to find \( \angle DBC \). Let's denote:

• \( \angle DBC \) as \( x \)

Using the angle addition around point \( B \):

\[ \angle ABC + \angle ABD + \angle DBC = 360^\circ \]

Substitute the known values:

\[ 155^\circ + 60^\circ + x = 360^\circ \]

Now, combine the known angles:

\[ 215^\circ + x = 360^\circ \]

To find \( x \), subtract \( 215^\circ \) from both sides:

\[ x = 360^\circ - 215^\circ \]

\[ x = 145^\circ \]

Therefore, the measure of \( \angle DBC \) is

\[ \boxed{145^\circ} \]