Answer:
m∠ABD=116°
m∠DBC=64°
Explanation:
The sum of the two angles given equals 180°. To find the two angle measures, use the following equation:
m∠ABD+m∠DBC=180°
For this problem, m∠ABD=(7x+67)° and m∠DBC=(8x+8)°. So,
(7x+67)°+(8x+8)°=180°
15x+75=180
15x=105
x=7
Next, substitute x=7 into the original expressions for the angle measures.
m∠ABD=(7(7)+67)°
m∠ABD=(49+67)°
m∠ABD=116°
and
m∠DBC=(8(7)+8)°
m∠DBC=(56+8)°
m∠DBC=64°