What is the scale factor from Polygon A to Polygon B? Explain your reasoning.
1 answer:
A. Scale factor = 2
B. The missing length of each side of polygon B are: 3 and 5
C. The measure of each angle that is marked in Polygon A are:
53° and 82°.
<h3>How to Find the Scale Factor of Similar Polygons?</h3>Similar polygons have the same shape and size, hence, the length of their corresponding sides are proportional to each other, while their corresponding angle measures are congruent to each other.
Scale factor = dimension of new polygon / corresponding dimension of original polygon.
A. From the given image of the two polygons, we have the following:
Dimension of new polygon, A = 5
Corresponding dimension of original polygon, B = 2.5
Scale factor = 5/2.5
Scale factor = 2
B. The missing length of each side of polygon B are:
1.5 × scale factor = 1.5 × 2 = 3
2.5 × scale factor = 2.5 × 2 = 5
C. Both polygons are similar, therefore, they will have the same angle measures.
The measure of each angle that is marked in Polygon A are:
53° and 82°.
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Answer:
The option is C i.e 115°, 65°. proof is given below.
Step-by-step explanation:
Given:
ABCD is a quadrilateral.
m∠ A = 100 + 5x
m∠ B = 77 - 4y
m∠ C = 106 + 3x
m∠ D = 47 + 6y
To Prove:
ABCD is a parallelogram if opposing angles are congruent by finding the measures of angles.
m∠ A = m∠ C and
m∠ B = m∠ D
Proof:
ABCD is a quadrilateral and is a parallelogram if opposing angles are congruent.
∴ m∠ A = m∠ C
On substituting the given values we get
∴ 100 + 5x = 106 +3x
∴
m∠ A = 100 + 5x = 100 + 5 × 3 =100 + 15 = 115°
m∠ C = 106 + 3x = 106 + 3 ×3 =106 + 9 = 115°
∴ m∠ A = m∠ C = 115°
Similarly,
∴ m∠ B = m∠ D
77 - 4y = 47 + 6y
10y = 77 - 47
10y =30
∴
m∠ B = 77 - 4y =77 - 4 × 3 = 77 - 12 = 65°
m∠ D = 47 + 6y = 47 + 6 × 3 = 47 + 18 = 65°
∴ m∠ B = m∠ D = 65°
Therefore the option is C i.e 115°, 65°