What is the measures and reason?

All these lines are parallel (the lines with the red arrow mark on the right side), so that means you can apply the alternate interior angles theorem, vertical angles theorem, corresponding angles theorem, alternate exterior angles theorem, etc.

The diagram shows that the given angle is 133 degrees. The given angle is a corresponding angle to the angle right next to angle 1, so that means the measure of the angle next to angle 1 is equal to 133 degrees.

Using the consecutive interior angles theorem, we can find the measure of angle 1 because it is a consecutive interior angle to the angle adjacent to it (which we found was 133 degrees). This means that angle 1 and the angle adjacent to it (133 degrees) should add up to 180 degrees because they are supplementary.

angle 1 + 133 = 180

Subtract 133 from both sides to solve for angle 1.

angle 1 = 47

Using the consecutive interior angles theorem, we know that angle 1 is equal to 47 degrees.

We can solve for the measure of angle 2 because since the given angle of 133 degrees and angle 2 are on opposite sides of the transversal and between the parallel lines, they are alternate interior angles. By the alternate interior angles theorem, angle 2 is equal to 133 degrees.

Finally we can solve for the last angle, angle 3. Angle 3 is a consecutive interior angle to angle 2, so by the consecutive interior angles theorem, angle 3 and the measure of angle 2 should add up to 180 degrees (because they are supplementary).

angle 3 + 133 = 180

Solve for angle 3 by subtracting 133 from both sides of the equation.

angle 3 = 47

By the consecutive interior angles theorem, angle 3 is equal to 47 degrees.

5.5

step-by-step explanation:

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.