Find the length of lm. show your work.

LM = 20

Step-by-step explanation:

Use the Sine rule to calculate the length of LM

We require to find ∠N using sum of angles in a triangle.

∠N  = 180° - (53 + 44)° = 180° - 97° = 83°, then

= ( cross- m ultiply )

LM × sin44° = LN × sin83°, that is

LM × sin44° = 14 × sin83° ( divide both sides by sin44° )

LM = = 20

< 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⭐

95.03 is the answer. hope this !