If m∠ABC

Question

is 160°
, and m∠ABD
is 92°
, what is the angle measure of DBC
? ∠ABD
and ∠DBC
are adjacent angles inside ∠ABC
.(1 point)
Responses

160°
160 degrees

92°
92 degrees

80°
80 degrees

68°

Answer 1

To find the measure of angle DBC, we can use the fact that the sum of the measures of adjacent angles ∠ABD and ∠DBC is equal to the measure of angle ∠ABC.

The relationship can be expressed as:

\[ m∠ABC = m∠ABD + m∠DBC \]

Substituting the given values:

\[ 160° = 92° + m∠DBC \]

Now we can solve for m∠DBC:

\[ m∠DBC = 160° - 92° \] \[ m∠DBC = 68° \]

Therefore, the measure of angle DBC is:

68°