A side of the triangle below has been extended to form an exterior angle of 155°. Find the value of xx.

Step-by-step explanation:

Find a similar diagram attached

Let the exterior angle be 155°

The sum of interior angle is equal to the sum of the exterior angle of the triangle

Interior angle are angles inside the triangles

Sum of interior angles = 90 + x

Exterior angles are those outside the triangle.

Exterior angle = 155°

Since sum of interior = exterior, hence;

90 + x = 155

x = 155 - 90

x = 65°

Hence the value of x is 65°

Note that the same concept can be used for any other triangle extending to form an exterior angle

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)