Find the value of x. Give reasons to justify your solution-

Answer:

x = 34

Step-by-step explanation:

∠ PSR and ∠ TSU are vertical angles and congruent, then

∠ PSR = 4x, thus ∠ PSQ = x

The exterior angle of a triangle is equal to the 2 opposite interior angles.

∠ SQR is an exterior angle of Δ PQS , thus

x + x = 68

2x = 68 ( divide both sides by 2 )

x = 34

Answer:

X = 34°

Step-by-step explanation:

In order to solve this question we will need to know the following, when two lines intersect the opposite angles at that point are equal to each other, that the sum of all angles of a triangle is 180 degrees, and that the angle of a straight line is equal to 180 degrees.

Frist we will have to notice that ∠TSU is equal to ∠PSR, because they are opposite to each other (If you would like to understand this more you can research on a topic call "vertical angels"). Now it is important to understand the following.

∠PSR  = ∠PSQ + QSR

Since ∠PSR = ∠TSU = 4x, ∠QSR = 3x ⇒

⇒ ∠PSR  = ∠PSQ + QSR

   4x = ∠PSQ + 3x

   4x - 3x = ∠PSQ

   x = ∠PSQ

Now, since the sum of all angles in a triangle is equal to 180 we can now say the following:

∠QPS + ∠PSQ + ∠PQS = 180°

In order to find out what PQS is equal to we need to use our knowledge about the angel of a strait line (the angel of a strait line is equal to 180°).

So now we can say the following:

180° = ∠PQS + SQR

∠PQS = 180° - ∠SQR

Since we know that ∠SQR = 68° ⇒

⇒∠PQS = 180° - ∠SQR

  ∠PQS = 180° - 68°

  ∠PQS = 112°

Since ∠QPS = x, PSQ = x, and ∠PQS = 112° ⇒

⇒ ∠QPS + ∠PSQ + ∠PQS = 180°

   x + x + 112° = 180°

  2x = 180° - 112°

  2x = 68°

  x = 34°

Ian bought a cup of coffee. At first, he sipped slowly. As it cooled down, he drank more quickly. The last bit was cold, and he dumped it out

HELP IM BEING TIMED!!!!!

Answer The Question Below:

Question 15
If you have these three lengths 6cm,7cm,6cm can they make a Triangle?
O True
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Suppose that you own a compact car

that you bought new for 18,000 dollars.

The value of this particular make of car is

known to depreciate at a rate of 20%

per year.

Define a unit for each quantity in the

worksheet. Then enter a variable for

the time since you bought the car new