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castortr0y [4]
3 years ago
15

Find angle m and angle n

Mathematics
1 answer:
san4es73 [151]3 years ago
5 0

Answer:

m∠M = 79°

m∠N = 66°

Step-by-step explanation:

∠MPN is supplementary to ∠MPQ, so m∠MPN = 35

The sum of the measures of a triangle is 180.

So, m∠M + m∠N + m∠MPN = 180

5y + 4 + 4y + 6 + 35 = 180

9y + 45 = 180

9y = 135

y = 15

m∠M = 5y + 4 = 5(15) + 4 = 75 + 4 = 79

m∠N = 4y + 6 = 4(15) + 6 = 66

Another way to do this problem, which is easier, is to know that an exterior angle of a triangle is equal to the sum of the two remote interior angles.

That means 5y + 4 + 4y + 6 = 145

                      9y + 10 = 145

                      9y = 135

                         y = 15

From knowing the value of y you can now find the measures of angles M and N

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Quadrilateral ABCD is dilated by a scale factor of 1 over 3 centered around (1, 2). Which statement is true about the dilation?
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<em>Note: Since you missed to add the figure. So, after a little research I am kind of able to find the figure and hence, assuming it as a reference. Hence, I am attaching the figure and solution of that figure is also visible in the same figure.</em> Please check the attached figure (a)

Answer:

Segment B'D' will be parallel to segment BD and will be shorter than segment BD. Please see the attached figure (a) for better understanding.

Step-by-step explanation:

As we know that there are certain rules when a quadrilateral is dilated by a certain scale centered around a certain point.

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Let suppose P(a, b) is the point.

The dilation rule by a scale factor of 1 over 3 or (1/3) centered around (1, 2) is

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Hence,

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The attached figure show that if we draw the all these points in the coordinate plan i.e. A(1, 2), B(2, 3), C(4, 2), D(2, 1) and A'(1, 2), B'(4/3, 7/3), C'(2, 2), D'(4/3, 5/3), we can determine that Segment B'D' will be parallel to segment BD and will be shorter than segment BD.

<em>Keywords: dilation, quadrilateral, segment</em>

<em> Learn more about dilation from brainly.com/question/7569824</em>

<em> #learnwithBrainly</em>

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<h2>c. 2</h2>

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