Question

Fiona is drawing polygons on a computer. She wants to map a regular 9-sided polygon back onto itself using a reflection. Which set of lines can Fiona choose from for her line of reflection?

A.
any line passing through the center of the polygon

B.
any perpendicular bisector of one of the sides

C.
any line joining the midpoints of any two sides

D.
any line parallel to a side of the polygon

Answer 1

Answer:

In △ABC AB=AC

⇒∠B=∠C (Angles opposite to equal sides are equal)

Now using angle sum property

∠A+∠B+∠C=180

∘

⇒80

∘

+∠C+∠C=180

∘

⇒2∠C=180

∘

−80

∘

⇒∠C=

2

100

∘

=50

∘

now ∠C+∠x=180

∘

(Angles made on straight line (AC) are supplementary)

⇒50

∘

+∠x=180

∘

⇒∠x=180

∘

−50

∘

=130

∘

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