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Chapter 3: Q43. (page 115)

In an octagon the sum of the measures of the interior angles is _?_.

Short Answer

Expert verified

In an octagon the sum of the measures of all interior angles is1080.

Step by step solution

01

Step 1. Find the formula that can be used.

The sum of measures of all interior angles of a convex polygon with n sides =(n鈭�2)脳180.

02

Step 2. Find the number of sides of an octagon.

For an octagon, the number of all sides (n)=8.

03

Step 3. Calculate the sum of measures of all interior angles of an octagon.

The sum of all interior angles for n=8

(n鈭�2)脳180=(8鈭�2)脳180=6脳180=1080

Hence, the sum of all interior angles of an octagon is 1080.

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Most popular questions from this chapter

  1. What is the measure of each interior angle of a regular pentagon?
  2. Can you tile a floor with tiles shaped like regular pentagons? (ignore the difficulty in tiling along the edges of the room.)

Alan tried to prove Postulate 10 as shown below. However, he did not have valid proof. Explain why not.

If two parallel lines are cut by a transversal, then corresponding angles are congruent.

Given k鈭�l; transversal tcuts kand I

Prove: 鈭�1鈮�鈭�2

Statement

Reason

1.k鈭�l

Given

2.鈭�3鈮�鈭�2

If two parallel lines are cut by transversal then alt. int. 鈭�sare鈮�

3.鈭�1鈮�鈭�3

Vert. 鈭�sare鈮�

4.鈭�1鈮�鈭�2

Transitive Property

Find the value of x.

Copy and complete the proof of Theorem 3-4. Given: Transversal tcuts Iand n;

t鈯�l;l鈭�n

Prove: t鈯�n

Complete.

11. If the measure of each angle of a polygon is 174, then the measure of each exterior angle is?炉 and the polygon has?炉 sides.
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