In the figure, ∆abc ~ ∆def. solve for x
a) x = 1.5
b) x = 6
c) x = 4
d) x = 5.5

Option B x=6 units

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

Triangles ABC and DEF are similar

therefore

∠A≅∠D

∠B≅∠E

∠C≅∠F

and

AB/DE=BC/EF=AC/DF

Find the value of x

AB/DE=BC/EF

substitute the given values

x/3=16/8

x=3*16/8

x=6 units

< 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⭐