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slavikrds [6]
3 years ago
7

Find x and y and explain your answer

Mathematics
1 answer:
MrRissso [65]3 years ago
6 0

Answer:

x = <u>30</u>

y = <u>59.33</u>

Step-by-step explanation:

We have Redrawn the diagram by naming the quadrilateral.

Now According to redrawn diagram;

∠ A = 90°

∠ B = (2y-3)\°

∠ C = 3x\°

∠ D = (y+5)\°

We need to find the value of 'x' and 'y'.

Solution:

Now we know that;

"If a quadrilateral whose all four sides or vertices touches the circle then it is said to be cyclic quadrilateral."

The Given diagram is a Cyclic Quadrilateral.

Now By Properties of Cyclic Quadrilateral which states that;

"Sum of the angles of opposite side of quadrilateral is always 180°."

So we can say that;

∠ A + ∠ C = 180°

∠ B + ∠ D = 180°

Substituting the values we get;

\angle A + \angle C = 180\°\\\\90+3x=180\\\\3x=180-90\\\\3x=90\\\\x=\frac{90}{3} = 30

Also

\angle B + \angle D =180\°\\\\2y-3+y+5=180\\\\3y+2=180\\\\3y=180-2\\\\3y=178\\\\y=\frac{178}{3} =59.33

Hence The Value of x is 30 and y is 59.33.

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Right triangle ABC and right triangle ACD overlap as shown below. Angle DAC measures 20 degrees and angel BCA measures 30 degree
alexdok [17]

The image of the question is attached below.

Given:

m∠DAC = 20° and m∠BCA = 30°

m∠ABC = 90° and m∠CDA = 90°

To find:

The value of x and y.

Solution:

In right triangle ABC,

m∠BAC = x° + 20°

Sum of the interior angles of a triangle = 180°

m∠BAC +m∠ABC + m∠BCA = 180°

x° + 20° + 90° + 30° = 180°

x° + 140° = 180°

Subtract 140° from both sides.

x° + 140° - 140° = 180° - 140°

x° = 40°

In right triangle ADC,

m∠ACD = y° + 30°

Sum of the interior angles of a triangle = 180°

m∠ACD +m∠CDA + m∠DAC = 180°

y° + 30° + 90° + 20° = 180°

y° + 140° = 180°

Subtract 140° from both sides.

y° + 140° - 140° = 180° - 140°

y° = 40°

The value of x is 40 and y is 40.

6 0
3 years ago
Evaluate.
Jlenok [28]
45 + 2 × [ (45 × 60) + 25]
45 + 2 × 2700 + 25
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5 0
3 years ago
Mike's monthly pay after taxes is $2,300.
wlad13 [49]

Step-by-step explanation:

100%=>$2,300

45%=>x

x=$2,300×45÷100=$1035

The pay left for other purposes

$2300-$1035=$1265

Or:

100%=>$2,300

55%=>x

x=$2,300×55÷100=$1265.

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3 years ago
Whats the quotient of simplest from for 5 wholes divide by 2\9 ?
posledela
Keep Change Flip!!!
Keep: the first fraction 5 or 5/1
Change: Division sign to multiplication sign
Flip (reciprocal): the second fraction
So you get 5/1*9/2= 45/2 which simplified to 22 1/2
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3 years ago
Solve the equation X3 equals -215
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Answer..

Step-by-step explanation:

4 0
2 years ago
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