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Vaselesa [24]
3 years ago
9

Meg constructed triangle POQ and then used a compass and straightedge to accurately construct line segment OS, as shown in the f

igure below:
Which could be the measures of angle POS and angle POQ?

Measure of angle POS is 25 degrees, measure of angle POQ is 40 degrees
Measure of angle POS is 25 degrees, measure of angle POQ is 30 degrees
Measure of angle POS is 20 degrees, measure of angle POQ is 40 degrees
Measure of angle POS is 20 degrees, measure of angle POQ is 30 degrees

Mathematics
2 answers:
jarptica [38.1K]3 years ago
8 0
In order to understand this question, one needs to understand the construction first. After creating POQ, Meg picks a radius r and makes a circle around O. There are 2 points where the circle meets the triangle. Then, she meets another radius and she makes a circle of radius s around each of the points on the triangle. The two circles cross at one point, as can be seen in the figure. Let's name the first two points A and B and let's name the last point S. We have that for the triangles OAS, OBS we have OA=OB=r, BS=AS=s and that OS is common to both. Thus by the S-S-S triangle equality theorem, the triangles are equal. Hence for the angles AOS=BOS, namely POS=QOS. Since POQ=POS+QOS, we have that POS has to be half of POQ. The only consistent choice is the third one, POS=20 degrees and POQ=40 degrees.
IrinaK [193]3 years ago
8 0

The <em><u>correct answer</u></em> is:

Measure of angle POS is 20 degrees, measure of angle POQ is 40 degrees

Explanation:

OS is an angle bisector of ∠POQ.  This means it splits ∠POQ into two congruent pieces.  

This tells us that ∠POS+∠SOQ = ∠POS+∠POS = ∠POQ.

If m∠POS = 20, this means that m∠POQ = 20+20 = 40°.

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I need help finding the solution
Ilya [14]
<h3>Answer:  226 degrees</h3>

=====================================================

Explanation:

Notice the tickmarks on the segments in the diagram. This tells us that chords DC and CB are the same distance from the center. It furthermore means that DC and CB are the same length, and arcs DC and CB are the same measure

arc DC = arc CB

12x+7 = 18x-23

12x-18x = -23-7

-6x = -30

x = -30/(-6)

x = 5

---------------------

Use this x value to find the measure of arcs DC and CB

  • arc DC = 12x+7 = 12*5+7 = 67
  • arc CB = 18x-23 = 18*5-23 = 67

We get the same measure for each, which helps confirm we have the correct x value.

The two arcs in question add to 67+67 = 134 degrees. This is the measure of arc DCB. Subtract this from 360 to get the answer

arc DAB = 360-(arc DCB) = 360-134 = 226 degrees

I'm using the idea that (arc DCB) + (arc DAB) = 360 since the two arcs form a full circle.

7 0
3 years ago
Trying to find the missing segment to the triangle in the attached image.
Inga [223]

Answer:

44 units length

Step-by-step explanation:

The side splitter theorem states that if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally. Therefore:

20/10 = x/22

20/10*22 = x

44 = x

3 0
3 years ago
If you borrow $1,200 for 3 years at an annual interest rate of 4% how much will u pay?
Anastaziya [24]
I=Prt
I=$1,200(0.04)3
I=$144
7 0
3 years ago
12 is 90% of what number?<br><br><br> with steps
a_sh-v [17]

Answer:

<h3><u>Let's</u><u> </u><u>understand the concept</u><u>:</u><u>-</u></h3>
  • Here 12 is 90% of a number.
  • So we can say that 90% of That number is 12 .
  • In this way we can get the the number
<h3><u>Solution</u><u>:</u><u>-</u></h3>

Let,

the number=x

<h3>According to the question ,</h3>

{:}\longrightarrow\sf 90\% \:of \;x=12

  • We know 90%=90/100
  • so add it

{:}\longrightarrow\sf {\dfrac {90}{100}}\times x=12

{:}\longrightarrow\sf {\dfrac {90x}{100}}=12

  • Now use cross multiplication method

{:}\longrightarrow\sf 90x=12\times 100

{:}\longrightarrow\sf 90x=1200

  • Now interchange sides .

{:}\longrightarrow\sf x={\dfrac {1200}{90}}

{:}\longrightarrow\sf x={\dfrac {200}{15}}

  • Answer will come in decimals so we take approximate value.

{:}\longrightarrow\sf x=13.3

{:}\longrightarrow\sf x=approximately \:13

\thereforeThe number is 13.

6 0
2 years ago
A gardener determines the cost of planting daffodil bulbs to be $2.40 per square foot. How much will it cost to plant daffodil b
deff fn [24]
The answer to your question is C) $144
5 0
3 years ago
Read 2 more answers
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