If angle jnp =2x+3 and angle knl =3x-17 and angle knj =3x+34 find the measure of each angle

m∠JNP=43°

m∠KNJ=94°

m∠KNL=43°

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

m∠JNP+m∠KNJ+m∠KNL=180° ----> by definition of supplementary angles

we have

m∠JNP=(2x+3)°

m∠KNJ=(3x+34)°

m∠KNL=(3x-17)°

substitute the values

(2x+3)°+(3x+34)°+(3x-17)°=180°

Combine like terms in the left side

(8x+20)=180

Subtract 20 both sides

8x=180-20

8x=160

x=20

Find the measure of m∠JNP

m∠JNP=(2x+3)°

substitute the value of x

m∠JNP=(2(20)+3)=43°

Find the measure of m∠KNJ

m∠KNJ=(3x+34)°

substitute the value of x

m∠KNJ=(3(20)+34)=94°

Find the measure of m∠KNL

m∠KNL=(3x-17)°

substitute the value of x

m∠KNL=(3(20)-17)=43°

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)