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Alecsey [184]
3 years ago
14

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

s. What are the values of X and Y?

Mathematics
1 answer:
alexdok [17]3 years ago
6 0

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.

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Answer:

y = x² − 6x − 27

Step-by-step explanation:

To distribute, you can use something called FOIL.  It stands for First, Outer, Inner, Last.

First, multiply the First term in each factor.

x · x = x²

Now multiply the Outer terms in each factor.

x · 3 = 3x

Next multiply the Inner terms in each factor.

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Finally, multiply the Last terms in each factor.

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Add them all up:

x² + 3x − 9x − 27

x² − 6x − 27

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Cameron bought a packet of 45 bars of chocolate.He ate one fifth of them on Tuesday.He ate a twelfth of the remaining bars on We
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