QS is an angle bisector, what is the value of x?

The value of x is 16

Step-by-step explanation:

The angle Bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle

In Δ QPR

∵ QS is the angle bisector

∵ PR is the opposite side

→ By using the rule above

∴ =

∵ PS = x and PQ = 30

∵ PR = 40

∵ RS = PR - PS

∴ RS = 40 - x

∵ RS = 40 - x and RQ = 45

→ Substitute them in the rule above

∴ =

→ By using the cross multiplication

∵ x × 45 = 30 × (40 - x)

∴ 45x = 30(40) - 30(x)

∴ 45x = 1200 - 30x

→ Add 30x to both sides

∵ 45x + 30x = 1200 - 30x + 30x

∴ 75x = 1200

→ Divide both sides by 75

∴ x = 16

∴ The value of x is 16

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: