To prepare for a party, Mark buys a small bunch of balloons for $4.00 and
1 answer:
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Answer:
The measure of one angle of a regular convex 20-gon is 162°
Step-by-step explanation:
* Lets explain how to solve the problem
- A convex polygon is a polygon with all the measures of its interior
angles less than 180°
- In any polygon the number of its angles equal the number of its sides
- A regular polygon is a polygon that is all angles are equal in measure
and all sides are equal in length
- The rule of the measure of an angle of a regular polygon is
, where m is the measure of each interior
angle in the polygon and n is the numbers of the sides or the angles
of the polygon
* Lets solve the problem
- The polygon is convex polygon of 20 sides (20 angles)
- The polygon is regular polygon
∵ The number of the sides of the polygon is 20 sides
∴ n = 20
∵ The polygon is regular
∴ All angles are equal in measures
∵ The measure of each angle is
∴
∴
∴
∴ m = 162
∴ The measure of one angle of a regular convex 20-gon is 162°
Answer:
nth term =
Step-by-step explanation:
Let us assume that the given sequence is a G.P.
Now, if the first term of the G.P. is a and the common ratio is r, then
Third term = .......... (1) and
20th term = ........... (2)
Now, dividing equation (2) with equation (1) we get
⇒
⇒ r = 1.2.
Hence, from equation (1) we get
a(1.2)² = 11
⇒ a = 7.639 (Approx.)
Therefore, the general term of the sequence i.e. nth term = (Answer)