1. If M is the midpoint, then LM and MN are equal to each other. So, 3x = 2x + 2. You can then solve that equation so find x, and then evaluate 3x to find the length of the LM.

2. The angles are supplementary, so their sum is 180 degrees. So, 5x + 10 = 2x - 5. Solve for x, and then evaluate 2x - 5 to find the angle measure.

3a. QPR and RPS are complementary, so their sum is 90 degrees.

3b. SPT is given. QPR and UPT are opposite angles, so their measures are equal. Add those two together to get SPU.

3c. QPU is opposite RPT, so they have equal measures. SPT is given, and you should know RPS by now, so you can find the sum of those to find the measure of QPU.

1. How did you get 5x+10=2x+2? And by finding the length of the line, do you mean finding LM?

2. What do you mean evaluate 2x-5? By finding x, do I combine like terms?

Thank you.

1. Sorry, I think I was looking at the second figure when I finished writing #1. I've the above comment to fix the typos.

2. Once you've found x, you need to find what 2x - 5 is. So, multiply x by 2 and then subtract 5, which gives the measure of angle DBC.

it's not that hard. HI out there. 

1)   M is the mid-point of LN.So, ML=MN

3x=2x+2

3x-2x=2

x=2

2)angle DBC +angleABD=180

5x+10+2x-5=180

7x+5=180

7x=175

x=23

3)Angle SPT=90 [given]

Angle RPQ=40 [given]

RT is a straight line

therefore all angles sum up to 180

Angle RPQ+SPT+RPS=180

Angle RPS+40+90=180

Angle RPS+130=180

a)Angle RPS=50

RU is a straight line, all angles on a straight line sum to 180

RPQ+QPU=180

UPQ+40=180

c)UPQ=140

Again QT is a straight line.

Angle TPU+QPU=180

Angle TPU+140=180

Angle TPU=40

therefore,Angle SPU=90+40

b)Angle SPU=130

Hope this helps.

Mahi