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Anni [7]
2 years ago
5

Find the angle measure. The measure of angle XYZ is

Mathematics
1 answer:
shutvik [7]2 years ago
6 0

Answer:

<h3>∠XYZ = 102</h3><h3></h3>

Step-by-step explanation:

<u>1st step is to solve x from ΔWXY</u>

∠W + ∠X + ∠Y = 180

where ∠W = 5x + 2

           ∠X = 7x + 4

           ∠Y = 180 - (15x - 18)

                 = 198 - 15x

now plugin values into the equation:

5x + 2   +   7x + 4  +  198 - 15x  = 180

combine similar terms:

5x + 7x - 15x = 180 - 2 - 4 - 198

simplify:

-3x = -24

x = -24 / -3

x = 8

<u>2nd step is to substitute x = 8 into ∠XYZ</u>

∠XYZ = 15x - 18

∠XYZ = 15(8)  - 18

∠XYZ = 102

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Answer:

<em>Area of polygon D = 10 square units</em>

Step-by-step explanation:

<u>Given:</u>

Polygon <em>C </em>has an area of 40 square units.

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<u></u>

<u>To find:</u>

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<u>Solution:</u>

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Let us consider this by taking examples:

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Area of a right angled triangle is given by:

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If scaled with a factor \frac{1}{2}, the sides will be 3, 4 and 5.

New area, A':

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  • Let us consider a rectangle now.

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Area of a rectangle, A = Length \times Width = 8 \times 10 = 80 sq units.

Now after scaling, the sides will be 4 and 5 units.

New Area, A' = 4 \times 5 =20 sq units

So, \bold{A' = \frac{1}4 \times A}

Now, we can apply the same in the given question.

\therefore Area of polygon D = \bold{\frac{1}{4}}\times Area of polygon C

Area of polygon D = \bold{\frac{1}{4}}\times 40 = <em>10 sq units</em>

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