To find the measure of angle \( DBC \), we can use the fact that the sum of the angles \( \angle ABC \) and \( \angle DBC \) equals \( 180^\circ \) since they are supplementary.
Given:
- \( m\angle ABC = 160^\circ \)
- \( m\angle ABD = 92^\circ \)
Since \( \angle ABD \) and \( \angle DBC \) are adjacent angles inside \( \angle ABC \), we can express \( m\angle ABC \) as follows:
\[ m\angle ABC = m\angle ABD + m\angle DBC \]
Substituting the known values:
\[ 160^\circ = 92^\circ + m\angle DBC \]
Now, solve for \( m\angle DBC \):
\[ m\angle DBC = 160^\circ - 92^\circ \] \[ m\angle DBC = 68^\circ \]
Thus, the measure of angle \( DBC \) is 68°.
The correct answer is A. 68°.
2 answers