Need help ASAP giving 25 points

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 five times

rusak2 [61]

Answer:

$x=30\\y=68\\z=82$

Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)

$y+z=5x$

The third angle is 14 more than the second

$z=y+14$

And remember that the sum of these three angles must be equal to 180.

$x+y+z=180$

Let's take these equations

$y+z=5x\\z=y+14\\x+y+z=180$

If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

$x+y+z=180\\x+(y+z)=180\\x+(5x)=180$

Distribute the + sign

$x+5x=180$

Combine like terms;

$6x=180$

Divide by 6.

$x=\frac{180}{6}\\ x=30$

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example $z=y+14$

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

$x+y+z=180\\30+y+(y+14)=180$

Distribute the + sign and Combine like terms;

$30+y+y+14=180\\44+2y=180\\$

Subtract 44 to isolate 2y.

$2y=180-44\\2y=136$

Now divide by 2.

$y=\frac{136}{2}\\ y=68$

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

$x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82$

5 0

3 years ago

If two angles are a linear pair, then they add to equal 180

kondor19780726 [428]

Answer:

True i think

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

What is 5 1/4 . 1 5/9 ? Express the answer in simplest form

Agata [3.3K]

$5\dfrac{1}{4}\cdot1\dfrac{5}{9}=\dfrac{5\cdot4+1}{4}\cdot\dfrac{1\cdot9+5}{9}=\dfrac{21}{4}\cdot\dfrac{14}{9}=\dfrac{7}{2}\cdot\dfrac{7}{3}\\\\=\dfrac{7\cdot7}{2\cdot3}=\dfrac{49}{6}=\dfrac{48+1}{6}=\boxed{8\dfrac{1}{6}}$

8 0

2 years ago

There are already 1,200 gallons of water in a swimming pool. If water is filling the pool at a rate of 30 gallons per minute, wh

Alika [10]

Answer:

n = 30m + 1,200

Step-by-step explanation:

let n = gallons

m = minutes

There are 30 gallons per minute, so 30 is multiplied by the minutes, and because there are already 1,200 gallons of water, you add 1,200

4 0

2 years ago

Need help w this onee thankss!!

skad [1K]

Step-by-step explanation:

if you draw an imaginary perpendicular line across the figure from the vertex which joins the line of 2 cm with the line that is making an angle of X then you can see that this figure is made up of two figures that is a triangle and a rectangle.

now from the angle given i.e X.

perpendicular= 5 cm

base = 14 -2= 12 cm

hypotenuse= ?

we know that,

h² = p²+b²

= 5²+12²=169

h= √169

h= 13

again,

cos X = b/h

= 12/13

6 0

2 years ago