Question

1. how many diagonals can you draw from one vertex in a polygon with 35 sides? 4. whats the total number of diagonals in a 35 - sided polygon?

Explanation:

Step1: Recall the formula for diagonals from one vertex

The number of diagonals from one vertex of an $n$-sided polygon is $n - 3$.

Step2: Substitute $n = 35$

For a 35 - sided polygon, the number of diagonals from one vertex is $35- 3$.
$35 - 3=32$

Step3: Recall the formula for total diagonals

The formula for the total number of diagonals in an $n$-sided polygon is $\frac{n(n - 3)}{2}$.

Step4: Substitute $n = 35$

Substitute $n = 35$ into the formula: $\frac{35\times(35 - 3)}{2}=\frac{35\times32}{2}$.
$\frac{35\times32}{2}=35\times16 = 560$

Answer:

1. 32
2. 560