The measure of angle 1 is (3x + 10)° and the measure of angle 4 is (4x – 15)°. Vertical and parallel lines c, d, and e are cut by diagonal transversal a. On line c where it intersects with line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 2, 4, 3, 1. On line b where it intersects with line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 6, 8, 7, 5. What is the measure of angle 7? °

95 degrees

Step-by-step explanation:

since angles 1 and 4 are vertical angles, they are congruent

3x+10=4x-15

3x-4x=-15-10

-x=-25

x=25

x=25 degrees

angles 4 and 7 are supplementary due to them being alternate exterior angles

lets find the measure of angle 4:

4x-15

4*25-15

100-15

85 degrees

Now, lets find the angle measure of angle 7:

85+x=180

x=180-85

x=95

So, the angle measure of angle 7 is 95 degrees

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is