Answer:
Only Statements B, C, D and half of statement F are correct.
Explanation:
The full correct question and image is attached to this solution.
The original polygon is polygon P. So, we're to select the true statements about any scaled copy Q of polygon P.
The angles of the polygon P include 90°, 125°, 35°, 250°, 80° and 135°.
The lengths of the polygon P aren't provided.
We should note that the scaled copy of any shape only has length of the original shape scaled up or down (depending on the scaling used). The angles between the sides remain the same in the scaled copy.
So, we check each statement out one by one.
Statement A
For copy Q of the polygon P, the side lengths are all whole numbers.
This will not always be true. The scaled representation of a shape usually can be fractional; thereby leading to fractional lengths on the scaled copy.
Even if the scaled copy isn't fractional, the length of the sides of polygon P (which weren't given might be fractional too); thereby leading to fractional lengths on the scaled copy.
So, statement A isn't true.
Statement B
For copy Q of polygon P, the angle measures are all whole numbers.
The angles measures of a scaled copy are still the same as the angle measure of the original shape. And since the angle measures of the original polygon P are all whole numbers (90°, 125°, 35°, 250°, 80° and 135°), all the angle measures of copy Q are all whole numbers.
Statement B is true.
Statement C
Q has exactly 1 right angle.
Since the original polygon P has only one right angle, the scaled copy Q too will have exactly one right angle too.
Statement C is true.
Statement D
If the scale factor between P and Q is (1/5), then each side length of P is multiplied by (1/5) to get the corresponding side length of Q.
This is the exact definition of scaling.
The side lengths of scaled copy Q = (lengths of corresponding sides on polygon P) × (scale factor)
Statement D is true.
Statement E
If the scale factor is 2, each angle in P is multiplied by 2 to get the corresponding angle in Q.
No matter what the scale factor is, the angle measures of the scaled copy are always the same as the angle measures of the original copy.
So, the scale factor being 2 does not mean that the angles of the scaled copy doubles.
Statement E is not true.
Statement F
Q has 2 acute angles and 3 obtuse angles.
An acute angle is one that is less than 90° while an obtuse angle is one that is greater than 90° but less than 180°.
We have established that the angle measures of scaled copy Q are the same as those of polygon P.
The angles of scaled copy Q are 90°, 125°, 35°, 250°, 80° and 135°.
The acute angles (angles less than 90°) are 35° and 80° (two).
The obtuse angles (angles greater than 90°, but less than 180°) are 125° and 135° (two).
Scaled copy Q has 2 acute angles and 2 obtuse angles.
Statement F is partially correct, but wrong on the number of obtuse angles.
So, only Statements B, C, D and half of statement F are correct.
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