Compute the missing angles in the given figure.

the figure shows a triangle upperword lmn. the side ln is produced in both the directions and a point upper p is labeled on the portion of line produced with upper n. the side mn is produced in both the directions and a point upper o is labeled on the portion of line produced with upper n. the angle upperword pnm is labeled as 142 degree, the angle upperword mln is labeled as 90 degree and the angle upperword nml is labeled as x.

missing angle measure (in degrees)
∠
m
32


∠
l
n
m

Part 1:

∠LNM = 38°

Part 2:

∠  M = x = 52°

Step-by-step explanation:

Part 1:

A straight line (straight angle) has a measure of 180°

From the figure, we can say:

PNM + LNM = 180

142 + LNM = 180

∠LNM = 180 - 142 = 38°

Part 2:

Now, for angle M, we recognize that sum of 3 angles of a triangle is 180°

Thus,

90 + 38 + x = 180

128 + x = 180

x = 180 - 128

x = 52°

e.

step-by-step explanation:

because there are always 10 numbers in a phone number.

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.