Question

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

Can someone explain how to do it also?

Answer 1

Answer:

ROS=72° TOS=83°

Step-by-step explanation:

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

7x-6=155

7x=161

x=23

4(23)-20=72

3(23)+14=83

Answer 2

Answer:

ROS is 72 degrees.

TOS is 83 degrees.

Step-by-step 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!