Use the figure above for exercises 1 and 2 1) what does = ? 2) m

A straight line is 180°. The angles of QRT (2x + 33) and TRS (5x - 21) make up the 180° angle. So you can do:

∠QRT + ∠TRS = 180°

(2x + 33) + (5x - 21) = 180°

2x + 33 + 5x - 21 = 180 Combine like terms

7x + 12 = 180   Subtract 12 on both sides

7x = 168   Divide 7 on both sides

x = 24

Now that you found x, you can find the angles of QRT and TRS.

m∠QRT = 2x + 33

           = 2(24) + 33

           = 48 + 33

∠QRT = 81°

m∠TRS = 5x - 21

          = 5(24) - 21

          = 120 - 21

∠TRS = 99°

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