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Charra [1.4K]
3 years ago
14

The sum of the measures of the interior angles of a convex polygon is 3960°.

Mathematics
1 answer:
scZoUnD [109]3 years ago
5 0

Step-by-step explanation:

The sum of the interior angles of a convex regular polygon is 180 times (n-2), where n is the number of sides. Since we already know the sum, we can write 3,960 = 180(n-2). If you solve for n in this equation, you will have the number of sides.

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complementary sums until 90 degrees

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Prove that angle W is congruent to angle Y with a two column proof.
iren2701 [21]

Statement 1: WXYZ is a kite

Reason 1: Given

Statement 2: WX = XY and WZ = YZ

Reason 2: Definition of a kite

Statement 3: XZ = XZ

Reason 3: Reflexive property

Statement 4: Triangle WXZ = Triangle YXZ

Reason 4: SSS Congruence

Statement 5: Angle W = Angle Y

Reason 5: CPCTC

-------------------------------------------------------------------------

Extra notes:

* A kite is a quadrilateral that has two pairs of adjacent congruent sides. In this case, WX and XY is one pair of congruent sides that are adjacent (ie next to each other). So that's why WX = XY. Similarly, WZ = YZ is the second pair of adjacent congruent sides.

* Draw in a segment from point X to point Z to help form two triangles. The two triangles are congruent as proven in statement 4. One triangle is a reflection over the line XZ to get the other triangle.

* Due to this reflection, angle W reflects over line XZ to get angle Y. Proving that angle W = angle Y

* SSS means "side side side", basically saying "you use three pairs of congruent sides to prove two triangles congruent".

* The acronym CPCTC stands for "corresponding parts of congruent triangles are congruent"

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