Determine the unknown angles in the diagram above. !

A

a and 143 are supplementary. So a + 143 = 180

a + 143 = 180              Subtract 143 from both sides.

a = 180 - 143

a = 37

B

b and 143 are vertically opposite angles and are equal

b = 143 degrees.

C

Interior angles on the same side of a transversal for parallel lines are supplementary

b + c = 180

143 + c = 180

c = 37

D

c + d + 85 = 180 degrees

37 + d + 85 = 180

d + 122 = 180

d = 180 - 122

d = 58

E

e = c They are vertically opposite.

e =37

F

All triangles have 180 degrees.

e + f + 90 = 180 degrees.

37 + f + 90 = 180

f  +  127 = 180

f = 180 - 127

f = 53

G

G and 48 are opposite 2 equal sides. So G and 48 are equal

G = 48

H

h + 48 + 48 = 180

h + 96 = 180

h = 84

K

K and H are supplementary

K + H = 180

k + 84 = 180

k = 95

M

m+ k + d  = 180

M + 95 +  58 = 180

M + 143 = 180

M = 37

P

the top angle is 2*m and 2m is bisected. You are using the m on the left.

P + 85 + M = 180

P + 85 + 37 = 180

P + 122 = 180

p = 180 - 122

p = 58

R

r + p are supplementary.

r + p = 180

r + 58 = 180

r = 180 - 58

r = 122

S

s + r + c + b = 360  All quadrilaterals have 360 degrees.

s + 122 + 37 + 143 = 360

s + 302= 360

s = 360 - 302

s = 58

77

step-by-step explanation: