# Please solve the question in a neat manner

First we join B to D.

In triangle BCD, BC=CD.

Thus angles CBD and CDB are equal. Let them be x.

x+x+110=180 Therefore, x=35 is the measure of angles CBD and CDB.

Also, arc BC=arc CD=arc AB=2*35=70.

Angle BAE=120 therefore arc BCDE=2*120=240 degrees.

Arc BCDE=arc BC+arc CD+arc DE= 70+70+arc DE=240

Thus arc DE = 100.

Arc BA+ arc AE+arc ED = 2*110=220

arc AE= 220-70-100=50.

2* angle ABC=arc AE=arc ED+ arc DC

Thus angle ABC = 220/2=110.

Similarly angle CDE can be found as 1/2(70+70+50) = 95.

You could similarly use this method to find the measure of the remaining required angles.

Regards.

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