In the regular decagon shown, what is the measure of angle 1?

36

Step-by-step explanation:

In any n sided polygon the sum of interior angles would be

(2n-4)90 degrees

There will be n exterior angles

The sum of interior and exterior would be

=180 n (by linear pair postulate)

Hence sum of exterior angles = (2n-4)90- 180 n=360

Hence in any polygon sum of exterior angles = 360

IN 10 sided polygon, i.e. decagon, sum of exterior angles =360

Hence each exterior angle = angle 1 = 360/10 = 36

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐

45

step-by-step explanation: