The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 15 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles. Do not include the degree symbol in your answer.

x = 45

y = 60

z = 75

Step-by-step explanation:

We can create three different equations with the given variables:

x + y + z = 180

y + z = 3 x

z = y + 15

then we can use this last equation to substitute for 'z" in the second equation:

y + z = 3x

y + y + 15 = 3 x

2 y + 15 = 3 x

x = 2/3 y + 5

Then we can re-write the first equation in terms of y and solve for this unknown:

2/3 y + 5 + y + y + 15 = 180

2/3 y + 2 y = 160

8/3 y = 160

y = 3 * 160 /8

y = 60

Then   x = 2/3 (60) + 5 = 45

so x = 45

and finally:   z = 60 + 15 = 75

so  z = 75

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

answer: what is the conflict?

step-by-step explanation:

*what has happened to new york city?

*what is in the time capsule?

* what did the kidz see that gave them hope?

*what will they do with what they find?

* how will they save the city?

* what challenges will they face along the way?

*what big choice will they make at the climax of the story?

* what lesson do they learn at the end of the story?