Benjamin bought tokens at a funfair. he used 3out if 8 of them at the ring toss booth and 2out of5 of the remaining tokens at the darts booth he then bought another 35 and had 10 tokens more then what he had at first how many tokens did he have at first

Let's assume he bought "x" tokens initially.

He spent 3 over 8 of them at ring toss game booth. So he used (3x/8) tokens there.

His remaining tokens after first game = x - (3x/8) = (5x/8) tokens.

He then spent 2 over 5 of them at darts game booth. So he spent (2/5)(5x/8) = (x/4) tokens there.

His left over tokens after second game = (5x/8) - (x/4) = (3x/8) tokens.

Now he bought another 35 tokens, his new balance = 35 + (3x/8)  tokens.

His new balance is ten more than his initially bought tokens.

So 35 + (3x/8) - x = 10

35 + (3x-8x)/8 = 10

35 + (-5x/8) = 10

(5x/8) = 35 - 10

(5x/8) = 25

5x = 25*8 = 200

x = 200/5 = 40

Hence, he bought initially 40 tokens.

< 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⭐