A nonagon is a polygon with 9 sides. What is the measure of each interior angle of a regular nonagon?
Select one:
a.
140°
b.
40°
c.
20°
d.
1260°
The measure of each interior angle of a regular nonagon is 140°.
Therefore, the correct answer is:
a. 140°
The exterior angle of a regular polygon is 10°. The number of sides the polygon must have is
Select one:
a.
38
b.
36
c.
18
d.
20
The sum of all exterior angles of a polygon is always 360°.
Therefore, to find the number of sides the polygon must have, we divide 360° by the measure of each exterior angle:
360° ÷ 10° = 36
So, the polygon must have 36 sides.
Therefore, the correct answer is:
b. 36
The set of information that can be used to determine an unknown side of a triangle using the cosine law is
Select one:
a.
The angle across from the unknown side, another angle and a side across from that angle
b.
The angle across from the unknown side and the two other sides.
c.
The two angles beside the unknown side.
d.
An angle beside the unknown side and the side across from it.
The correct answer is:
b. The angle across from the unknown side and the two other sides.
The cosine law states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the angle between them. Therefore, with the angle across from the unknown side and the two other sides, we can use the cosine law to determine the length of the unknown side.
Given:
A B equals D C
A E equals D E
C E equals B E
Prove:
triangle A C E approximately equal to triangle D B E
Graph 12a
Complete the proof below by dragging and dropping the appropriate reason.
Statement Justification
A B equals D C
blank
A B plus B C equals D C plus B C blank
A C equals D B blank
A E equals D E blank
C E equals B E blank
triangle A C E equals triangle D B E blank
Given Corresponding angles Angles that form a straight line add to 180 Substitution Alternate Interior Angles with respect to parallel lines, are equal Vertically Opposite Angles are equal Adding equal segments Addition ASA SSS SAS Corresponding sides of congruent triangles Common side
Statement Justification
A B equals D C Given
A B plus B C equals D C plus B C Adding equal segments
A C equals D B Substitution
A E equals D E Given
C E equals B E Given
triangle A C E equals triangle D B E ASA (Angle-Side-Angle)