Answer:
m∠DCQ=56°
Step-by-step explanation:
step 1
Find the measure of arc ABC
we know that
The inscribed angle is half that of the arc it comprises
so
m∠D=(1/2)[arc ABC]
we have
m∠D=78°
substitute and solve for arc ABC
78°=(1/2)[arc ABC]
156°=[arc ABC]
Rewrite
arc ABC=156°
step 2
Find the measure of arc DC
we know that
arc ABC+arc AD+arc DC=360° -----< by complete circle
substitute the given values
156°+92°+arc DC=360°
arc DC=360°-248°
arc DC=112°
step 3
Find the measure of angle DCQ
we know that
The inscribed angle is half that of the arc it comprises
so
m∠DCQ=(1/2)[arc DC]
we have
arc DC=112°
substitute
m∠DCQ=(1/2)[112°]=56°
