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The following figure is a quilt square composed of 8 identical parallelograms and 16 identical isosceles right triangles. What is the value of w°?

135°

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Step-by-step explanation:

If you look closely at the figure you can see it is divided into fourths, as squares.

We know that squares have a right angle measuring 90°.

We can also see that that 90° is split in two.

So let's do the math...

90° / 2 = 45°

Okay so the giant triangle holding w° has it's corner measuring 45°. So the little parallelogram in the triangle has one of it's angles measuring 45°. Since angles are congruent we know that another angle measures 45°. We also know that a parallelograms angles must always add up to the magic number of 360°. So our equation is

45° + 45° + w° + w° = 360°

90° + 2w° = 360°

90° - 90° + 2w° = 360° - 90°

2w° = 270°

2w° / 2 = 270° / 2

w° = 135°

Hope this helped you. It's really hard to explain through typing without being able to point at the model you gave

21

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answer:   c ?

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