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If a || b, m<2=63°, and m<9=105°, find the measure of missing angle m<1=?

worty [1.4K]

Given:

a.) ∠9 = 105°

b.) ∠2 = 63°

Step 1: Determine the measure of ∠10.

∠9 and ∠10 are Supplementary Angles. This means that the sum of the two angles is equal to 180°.

From this, we generate the following equation:

$\text{ }\angle9\text{ + }\angle10=180^{\circ}$

Let's then now proceed to find out the measure of ∠10.

$\text{ }\angle9\text{ + }\angle10=180^{\circ}$ $\text{ }105^{\circ}\text{ + }\angle10=180^{\circ}$ $\angle10=180^{\circ}\text{ - }105^{\circ}$ $\angle10=75^{\circ}$

Step 2: Determine the measure of ∠3.

∠10 and ∠3 are Alternate Exterior Angles. Under this, the two angles must be congruent.

$\text{ }\angle3\text{ = }\angle10$

Therefore,

$\text{ }\angle3\text{ = }\angle10$ $\text{ }\angle3=75^{\circ}$

Step 3: Determine the measure of ∠1.

∠1, ∠2 and ∠3 are also Supplementary Angles. This means that the sum of the three angles is equal to 180°.

Thus, we generate the equation below:

$\text{ }\angle1\text{ + }\angle2\text{ + }\angle3=180^{\circ}$

Let's now find the measure of ∠1,

$\text{ }\angle1\text{ + }\angle2\text{ + }\angle3=180^{\circ}$ $\text{ }\angle1\text{ + }63^{\circ}\text{ + }75^{\circ}=180^{\circ}$ $\text{ }\angle1\text{ + }138^{\circ}=180^{\circ}$ $\text{ }\angle1\text{ }=180^{\circ}\text{ - }138^{\circ}$ $\text{ }\angle1\text{ }=42^{\circ}$

Therefore, the measure of ∠1 is 42°.

8 0

1 year ago

A poker deck consists of cards ranked 2,3,4,5,6,7,8,9,10,J,Q,K,A, (13 different ranks) each in four suits, for a total of 52 dis

snow_lady [41]

Answer:

1) The probability to be given a Poker hand from a Pinochle deck is 0.7943

2) The probability that a hand that could be either a Poker hand or a Pinochle hand was given from a Pinochle deck is 0,3675

Step-by-step explanation:

Letc denote some events:

X = The hand i receive is from a Pinochle deck.

Y = The hand i receive is from a Poker deck

Z = The hand i receive is a Poker hand (from any deck)

Note that Y is the complementary event of X, therefore P(Y) = 1-P(X). Also, if Y is true so is Z, thus

P(Z | Y) = 1

we want to know P(Z | X) in order to resolve item 1)

The first card i receive from the five card hand can be anything, the second one can be anything different from the first card, and there is one copy of that card remaining in the deck, thus, 46 cards from the deck works, from a total of 47. After the second card was given, if it was different from the first card, we will have 2 cards that are copies of the 2 cards i receive, thus, there are, from the 46 remaining cases, only 44 are favourable. For the fourth card we will have 3 cards we dont want to draw, therefore we have 42 cases favourable over 45, and for the last card from a total of 44 cards, only 40 can help us.

With all this information, we have that the probability that a hand dealt from a Pinochle deck is a Poker hand is

P(Z | X) = 46/47* 44/46 * 42/45 * 40/44 = 112/141 = 0.7943

2) Since rach deck has a 1/2 probability of being selected, then

P(X) = P(Y) = 1/2.

In order to compute the probability that i draw a hand that could be either kind from a Pinochle deck, i will calculate first the probability that i draw a 'Pinochle hand' from a poker deck, in other words, if we call W the event that i drew a Pinochle hand, then we want P(W | Y)

Since a Poker deck has 52 cards and only 24 works for us, then P(W | Y) = 24/52 = 6/13 = 0.4615.

Note that P(W | X) = 1

Now, lets calculate what the problem wants, and that is P(X | W∩Z) (The probability to have drawn from a Pinochle deck a hand that could be either Poker or Pinochle. For that we use the Bayes Theorem

$P(X | W \cap Z) = \frac{P(W \cap Z |X) * P(X)}{P(W \cap Z |X) * P(X) + P(W \cap Z |Y) * P(Y)} = \frac{P(Z | X) * 1/2}{P(Z |X)*1/2+P(W|Y)*1/2} = \frac{6/26}{6/26+56/141} = \frac{423}{1151} = 0.3675$

[ Note that if X is given, then W always holds, thats why p(W∩Z|X) = P(Z|X). In a similar way P(W∩Z|Y) = P(W|Y), because given Y, Z always happens (a hand given from a Poker deck is always a poker hand). ]

We conclude that the probability that a hand that can be from any deck is in fact given from a Pinochle deck is 0.3675.

3 0

3 years ago

Anyone know how to solve by giving me not only an explanation in words but can show me the equation, to solve the problem below?

malfutka [58]

W=-4

Explanation
=============
1. Simplify the equation
$-2(w+10)=6w+12$ ====> $-2w-20=6w+12$

2. Subtract 6w from both sides.
$-2w-20-6w=6w+12-6w$ ====> $-8w-20=12$

3. Add 20 to both sides.
$-8w-20+20=12+20$ ====> $-8w=32$

4. Divide both sides by -8
$\frac{-8w}{-8}= \frac{32}{-8}$ ====> $w=-4$

4 0

3 years ago

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I've attached the question in the picture below.

ololo11 [35]

at a map scale of 1:1500, 12 centimeters on the map is equivalent to 1.8 kilometers on the ground.

step-by-step

since the scale is 1 to 15,000 you simply multiply it by the 12 cm

12cm × 15,000 = 180,000

but you still have to convert it to kilometers (the measurement on the ground).

to go from centimeters to kilometers move the decimal 5 place values to the left.

final answer

1.8 kilometers

5 0

4 years ago

Which circle is the graph of the equation (x+4)2+(y-5)2=4 circle a circle b circle c circle d

ollegr [7]

Answer:

you have to add

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers