Question

Please help! Polygon ABCDE rotates 45° clockwise about point F to form polygon FGHIJ, shown in the figure. Find the measure of each angle of polygon ABCDE.

mABC=?

mBCD=?

mDEA=?

mCDE=?

All 4 questions are either 90, 117, or 127

Answer 1

Answer:

mABC = 117 degrees

mBCD = 90 degrees

mDEA = 90 degrees

mCDE = 127 degrees

Step-by-step explanation:

Since ABCDE is congruent/equal to FGHIJ, then each angle corresponds with the angle in the other shape. I.E., A = F, B = G, C = H, etc. Finding the angle for ABC is finding the angle for FGH. This works only because there was no changing the places of the points individually. :)

Answer 2

The measure of each angle of polygon ABCDE is ∠ABC = 117°, ∠BCD = 90°, ∠DEA = 90°, ∠CDE = 127°.

What is a polygon?

A polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides. The sides of a polygon are made of straight line segments connected to each other end to end.  The interior angles of a polygon are equal to a number of sides.

For the given situation,

Polygon ABCDE rotates 45° clockwise about point F to form polygon FGHIJ.

The translation of rotation takes place here. So two polygons are congruent to each other.

Thus,

⇒ $\angle FGH=\angle ABC=117$

⇒ $\angle GHI=\angle BCD=90$

⇒ $\angle IJF=\angle DEA=127$

⇒ $\angle HIJ=\angle CDE=127$

Hence we can conclude that the measure of each angle of polygon ABCDE is ∠ABC = 117°, ∠BCD = 90°, ∠DEA = 90°, ∠CDE = 127°.

Learn more about polygons here

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