Find the values of x and y.
(10x – 4)º
16yº
(18y – 18)°
6(x + 2)°

The value of x is 4 and the value of y is 9

Step-by-step explanation:

In the attached pictures we can see that two lines are intersecting with each other and four angles are form. The angles opposite to each other are also called vertical angles.

The opposite pairs of angles are:

(10x-4)° and 6(x+2)°

(18y-18)° and 16y°

When two lines intersect each other, the vertical angles formed are congruent(Can also be called equal in measurement)

So,

Subtracting 6x from both sides

Adding 4 on both sides

Dividing both sides by 4

AND

Adding 18 on both sides

Subtracting 16y from both sides

Dividing both sides by 2

Hence,

The value of x is 4 and the value of y is 9

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true