2 lines intersect. where the 2 lines intersect, 4 angles are created. labeled clockwise, from uppercase right: angle 1 (3 x minus 1) degrees, angle 2 is blank, angle 3 (2 x + 9) degrees, and angle 4 is blank.
what are the numerical measures of each angle in the diagram?
∠1 and ∠3 measure degrees.
∠2 and ∠4 measure degrees

∠1 and ∠3 measure 29 degrees

∠2 and ∠4 measure 151 degrees

Step-by-step explanation:

we know that

Vertical angles are a pair of opposite angles formed by intersecting lines. They are always congruent to one another

see the attached figure to better understand the problem

we have that

m∠1=m∠3 -----> by vertical angles

m∠2=m∠4 -----> by vertical angles

m∠1+m∠2=180° ----> by supplementary angles (form a linear pair)

m∠3+m∠4=180° ----> by supplementary angles (form a linear pair)

In this problem we have

m∠1=(3x-1)°

m∠3=(2x+9)°

substitute in the expression

m∠1=m∠3

Solve for x

Find the measure of m∠1

m∠1=(3x-1)°

substitute the value of x

m∠1=(3(10)-1)=29°

Find the measure of m∠3

Remember that

m∠3=m∠1

therefore

m∠3=29°

Find the measure of m∠2

we have that

m∠1+m∠2=180°

m∠1=29°

substitute

29°+m∠2=180°

m∠2=180°-29°=151°

Find the measure of m∠4

Remember that

m∠4=m∠2

therefore

m∠4=151°

therefore

∠1 and ∠3 measure 29 degrees

∠2 and ∠4 measure 151 degrees

step-by-step explanation:

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}