answer: 240°
Calculate the measure of arc
D
E
^
DE
by doubling the measure of angle
∠
C
D
E
∠CDE. Given that
∠
C
D
E
=
6
0
∘
∠CDE=60
∘
, we have
m
D
E
^
=
2
×
6
0
∘
=
12
0
∘
m
DE
=2×60
∘
=120
∘
2 Find the measure of the remaining arc by subtracting the measure of arc
D
E
^
DE
from
36
0
∘
360
∘
, which is the total measure of a circle. So,
m
D
E
^
=
36
0
∘
−
12
0
∘
=
24
0
∘
m
DE
=360
∘
−120
∘
=240
∘
3 Match the calculated measure with the given options to find the correct answer. The correct answer is
24
0
∘
240
∘
, which corresponds to option A.
Therefore, the answer is
24
0
∘
240
∘
