Question

.If m∠ ROT = 155, what are m ∠ ROS and m∠TOS?

Can someone explain how to do it also?

Answer 1

ROS=72° TOS=83°

Explanation:

(4x-20)+(3x+14)=155

7x-6=155

7x=161

x=23

4(23)-20=72

3(23)+14=83

Answer 2

ROS is 72 degrees.

TOS is 83 degrees.

Explanation:

So we know that the measure of Angle ROT is 155.

Angle ROT is the combined value of Angle ROS and Angle TOS. In other words:

`ROT=ROS+TOS`

Substitute 155 for ROT, (4x-20) for ROS, and (3x+14) for TOS. Thus:

`155=(4x-20)+(3x+14)`

Combine like terms:

`155=(4x+3x)+(-20+14)`

Add:

`155=7x-6`

Add 6 to both sides:

`161=7x`

Divide both sides by 7:

`x=23`

So, the value of x is 23.

Now, plug that into each of the Angle equations to solve for each angle:

`ROS=4x-20\\ROS=4(23)-20`

Multiply:

`ROS=92-20`

Subtract:

`ROS=72`

Same thing for TOS:

`TOS=3x+14\\TOS=3(23)+14`

Multiply:

`TOS=69+14`

Add:

`TOS=83`

And we're done!