What are the measures of Angles a, b, and c? Show your work and explain your answers. (10 points)

a = 30, b = 60, c = 105

Step-by-step explanation:

a and the 30 degree angle are vertical angles, so they are equal. a = 30

a, b, and the 90 degree angle are all in a triangle together, so they add up to 180 degrees. 30 degrees + b + 90 degrees = 180, 120 degrees + b = 180,

b = 60 degrees

c and the 75 degree angle are on a line together, so they add up to 180:

c + 75 = 180

c = 105 degrees

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i

< 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⭐