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

geometry: triangles

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answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

10.416 m/s

step-by-step explantion:

distance=100m

time= 9.6s

average speed=100/9.6

=10.416 m/s