Question

I need help with solving #22

Answer 1

22)

Because OP and OR trisect <NOS

so <NOP = <POR

3x - 4y = x - y so 2x = 3y

<POR = <ROS

x - y = y - 10 so x = 2y - 10

Substitue x = 2y - 10 into 2x = 3y

2(2y - 10) = 3y

4y - 20 = 3y

y = 20

x = 2y - 10 = 2(20) - 10 = 30

x = 30 and y = 20

<ROS = y - 10 = 20 - 10 = 10

Answer

<ROS = 10°

Answer 2

When an angle is trisected, it is divided into 3 equal parts. That is,

... 3x -4y = x - y . . . . . ∠NOP = ∠POR

... x - y = y - 10 . . . . . ∠POR = ∠ROS

Add y to the second of these equations and you get

... x = 2y - 10

Substitute this into the first equation and you get

... 3(2y -10) -4y = (2y -10) -y . . . . substitute 2y-10 for x

... 2y -30 = y -10 . . . . . . . . . . . . . simplify

... y = 20 . . . . . . . . . . . . . . . . . . . add 30-y

... y - 10 = 20 -10 = 10 . . . . . . . . .substitute the value of y into the expression for the measure of angle ROS

m∠ROS = 10