# 3 Math questions please explain?!?

In as detailed as you can get, can you please explain to me how to finish solving these? THANK YOU SO MUCH!

1.) ABCD is an inscribed quadrilateral.

http://i38.tinypic.com/23ife4h.gif

a.) Find the values of x and y. Show all work.

b.) Find m angle B and m angle D.

I have 2x + 3y = 185 and 3x + y = 120

2.) http://i33.tinypic.com/29uwv4j.gif

In circle L, JK is a tangent and PM is a diameter. Find the measure of arc MN. Show all work

I have no clue for this one, please detail it so I can understand(:

3.) In circle V, RT is a diameter.

http://i34.tinypic.com/54d8hu.gif

a.) Find m angle STR and m angle SRT. Show all work.

b.) If ST = 22, find the length of the radius to the nearest tenths place. Show all work.

I have a.) STR = 44 and SRT = 46 .. I just need PART B ! (:

THANK YOU SO MUCH for answering! (: Best Answer will be given!

### 2 Answers

- Neil KelceyLv 69 years agoFavorite Answer
Q1)

You had:

➊: 3x + y = 120 ( ✔ :)

➋: 2x + 3y = 185 (✔ :)

So just solve the system of two equations, 2 unknowns (is this where you need the help?)

➊x3: 9x + 3y = 360

➋: 2x + 3y = 185

Subtract ➋ from ➊x3: 7x = 175 ➞ x = 175/7 = 25

Substitute x = 25 in ➊ ...

3(25) + y = 120

y = 120 – 75

y = 45

a) m∠B = 3y – 5 = 3(45) – 5 = 130º

b) m∠D = 2x = 2(25) = 50º

Q2)

Draw two radii: segments LJ and LN

Since ∠JKM = 20º, and KJ is tangent to circle L

➞ ∠KJL = 90º, and ∴ ∠JLK = 70º

➞ ∠JLM = 110º

We are given that ∠MQN = 44º ➞ ∠JQL = 44º

∴ In ∆JLQ, ∠LJQ = 180 – 110 – 44 = 26º

Since LJ = LN = radii of circle L, ∆LJL is isosceles ➞ ∠LJN = ∠LNJ = 26º

Since ∠JQN = 180º, and ∠JQL = 44º ➞ ∠LQN = 136º

In ∆LQN, ∠QLN = 180 – 136 – 26 = 18º

∠QLN is the central angle subtended by the arc MN and is 18º

Q3)

The link to your pic says the pic is no longer there ....????

Hope this has helped you! Cheers! :)

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- jarvinenLv 43 years ago
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