Triangle a b c is shown with its exterior angles. line c b extends through point d. line b c extends to form exterior angle that is 135 degrees. angle c a b is 75 degrees. what is m∠abc? m∠abc = 15° m∠abc = 45° m∠abc = 60° m∠abc = 75°

m∠ABC = 45°

Step-by-step explanation:

See the attached figure.

As shown in the figure

Line C B extends through point D to form the exterior angle that is 135 degrees.

So, m∠ABD = 135°

But m∠ABC + m∠ABD = 180°

∴m∠ABC = 180° - m∠ABD = 180° - 135°= 45°

Also, we should know that

m∠ABD = m∠BAC + m∠ACB

So, m∠ACB = 135° - 75° = 60°

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Very important note:

If we replaced the location of B and C

SO, m∠ABC = 60° and m∠ACB = 45°

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< 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⭐

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step-by-step explanation: