A hexagon (a six-sided figure) has four angles that have measures 152°, 108°, 140°, and 172º respectively. The
remaining two angles have the same angle measure.
Explain how to find the two missing angle measures.

74

Step-by-step explanation:

A polygon's angles add up to (n-2)*180, where n is the total number of sides, and a hexagon has 6 sides, which means its angles add up to 720 degrees.

Therefore, we can set up an equation where the missing angles, marked as x, and the rest of the angles add up to 720:

x+x+152+108+140+172=720

2x+572=720

2x=148

x=74

Therefore, the angles of the 2 missing angles is 74

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}