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Lady bird [3.3K]
3 years ago
8

In the figure, AB∥CD. Find x and y.

Mathematics
2 answers:
velikii [3]3 years ago
8 0

Answer:

y=131°

x=53°

Step-by-step explanation:

∠ ABD and ∠ BDC are supplementary.

The sum of the supplementary angles =180 °

thus y-4+x=180...........i

x and 37° are complementary, that  is, they add up to 90°

Thus, x=90-37=53°

Using this value in equation 1 we obtain:

y-4°+53° =180°

y= 180°-53°+4°

y=131°

Hatshy [7]3 years ago
5 0

Answer:

x  = 53°

y = 131°

Step-by-step explanation:

From the figure we can see a right angled triangle.

AB∥CD

<u>To find the value of x and y</u>

Consider the large triangle, by using angle sum property we can write,

90 + 37 + x = 180

127 + x = 180

x = 180 - 127

x  = 53°

Since AB∥CD and BD is a traversal on these parallel lines.

Therefore <ABD and < CDB are supplementary

we have x  = 53°,

x + (y - 4) = 180

53 + y - 4 = 180

y = 180 - 49 = 131°

y = 131°

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Find the value of x
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Last Option

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Now we solve for x from the equation

c ^ 2 = a ^ 2 + b ^ 2 -2abcosx\\\\\\14^2 = 11^2 + 19^2 -2(11)(19)cosx\\\\14^2 -11^2 -19^2 = 2(11)(19)cosx\\\\-286=2(11)(19)cosx\\\\cosx = \frac{-286}{2(11)(19)}\\\\x = arcos(\frac{-286}{2(11)(19)})\\\\x = 46.8\°

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Read 2 more answers
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