What are the numerical measures of each angle in the diagram? 1 and 3 measure degrees. 2 and 4 measure degrees. (3x - 1)º (2x + 9)°

Step-by-step explanation:

In the diagram shown, the measure of angle 1 is oppositely directed to angle 2 and oppositely directed angles are equal.

Hence <1 = <3

Given < 1 = 3x-1 and <3 = 2x+9

Hence 3x-1 =  2x+9

collect like terms

3x-2x = 9+1

x = 10°

Since <1 = 3x-1

on substituting x = 10

<1 = 3(10)-1

<1 = 30-1

<1 = 29°

<1+<2 = 180 (angle on a straight line)

29+<2 = 180

<2 = 180-29

<2 = 151°

Similarly, on substituting x = 10 into <3

<3 = 2x+9

<3 = 2(10)+9

<3 = 20+9

<3 = 29°

<3+<4 = 180 (angle on a straight line)

29+<4 = 180

<4 = 180-29

<4 = 151°

Just copying this over just in case others with similar questions turn this up in search results rather than the other, haha!
When you multiply or divide a negative by another negative, you get a positive. When it is a negative and a positive, it remains negative.
Assuming your question simplified into a equation (or number form? Been a while, haha!) is 32÷-2÷(-16÷4), it would end as a positive. Because you first divide the positive 32 by a negative 2, you get a negative. Because -16÷4 is in parenthesis, it is done because following the rest of the equation (P.E.M.D.A.S.!), it would be 32÷-2÷-4. Going from left to right, as you should, it results in a negative being divided by another negative, so you get a positive. 32÷-2÷(-16÷4) = 32÷-2÷-4 = -16÷-4 = 2!