There are ten chairs in a row. in how many ways can two people be seated so that they are not seated next to each other?

There are 368,947,264 ways to do so.

Step-by-step explanation:

Since we have given that

Number of chairs in a row = 10

Since two people can be seated so that they are not seated next to each other.

For number 8: One sit at either end of the row  

For number 7: One sit between last and first chair.  

so, the number of ways would be

Hence, there are 368,947,264 ways to do so.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°