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jekas [21]
3 years ago
14

In the figure shown, line AB is parallel to line CD. Part A what is the measure of angle x. Part b explain how you found the mea

surr of angle x by identifying the angle relationship that you used along the traversal

Mathematics
1 answer:
Lemur [1.5K]3 years ago
4 0

Answer:

Part A

x is 46°

Part B

Alternate angles are angles that are in relatively opposite locations relative to a transversal

Please see attached diagram showing alternate angles

Step-by-step explanation:

Part A

∠DRP  = 110° (Given)

∠QPA = 64° (Given)

∠QPR =

Given that AB is parallel to CD, we have;

∠DRP is congruent to ∠APR (Alternate angles to a transversal RP of parallel lines AB and CD)

Therefore, ∠APR = 115°

∠APR = ∠QPA + ∠QPR (Angle addition postulate)

∴ 115° = 64° +  ∠QPR

∠QPR = 110° - 64° = 46°

x = 46°

Part B.

Given that AB is parallel to CD, the lines common (that intersects) both lines are the transversal lines

The angles formed between the parallel lines and the transversal lines have special relationships based on their position with respect to each other

In the question, the angle 110° given between CD and the transversal RP, is found to at an alternate position to the angle ∠APR between the same transversal RP and AB and given that alternate angles are always equal, angle ∠APR is therefore also equal to 110°.

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nexus9112 [7]

Given, arc QR is congruent to arc LN and arc OP is congruent to arc VW.

And the expressions for each arc in the diagram also given as:

Arc QR = 2x - y, arc LN = 11 , arc OP= 10 and arc VW=5x+y.

Hence, we will get the system of equations as following:

Arc QR = Arc LN

2x - y = 11 ...(1)

Arc OP = Arc VW

5x + y = 10 ...(2)

Next step is to add the two equation to eliminate y so that we can solve the equations for x. Therefore,

2x+5x = 11 + 10

7x = 21

\frac{7x}{7} =\frac{21}{7} Divide each sides by 7.

So, x= 3

Now plug in x=3 in equation (2) to get the value of y.

5(3) + y = 10

15 + y =10

15 + y - 15 = 10 - 15 Subtracting 15 from each sides.

y = -5

So, x=3 and y =-5

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Let a, b, c be the lengths of sides of a triangle; a=4.8, b=0.23, and c is a whole number. Find c.
BaLLatris [955]

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3 years ago
2x - 2y = 12<br> 29. - 3y = -2
Sophie [7]

Olá boa tarde meu nome é "Guilherme" sou de Brasil e vou resolver a sua pergunta

a ) 2x - 2y = 12

{ a 2

{ b 2

{ c 12

<u>/</u><u>\</u> = b elevado 2 -4 a.c

<u>/</u><u>\</u> = (2) elevado 2 -4 . 24

<u>/</u><u>\</u> = 4 -4 . 24

<u>/</u><u>\</u> = 24

X = <u>-</u><u>b</u><u>+</u><u>/</u><u> </u><u>/</u><u>\</u><u> </u> = <u> </u><u>2</u><u> </u><u>-</u><u> </u><u>5</u>

2a 2

<u> </u><u>5</u>

2

<u> </u><u>5</u>

2

S = {20,10}

b) 29. - 3y = -2

{ a = 29

{ b = -3

{ c = -2

<u>/</u><u>\</u> = b elevado 2 -4 a.c

<u>/</u><u>\</u> = (-6) -4 . 58

<u>/</u><u>\</u> = -10 . 58

<u>/</u><u>\</u> = -48

X = <u> </u><u>b</u><u> </u><u>+</u><u> </u><u>/</u><u> </u><u>/</u><u>\</u><u> </u> = <u> </u><u>-</u><u>3</u><u> </u><u>+</u><u> </u><u>24</u><u> </u>

<u> </u><u>5</u>

3

<u> </u><u>5</u>

3

S = { 15,15}

Espero ter ajudado

2a 2

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Cloud [144]
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