The diagram for this problem is shown below. Point E is the intersection of the two diagonals and we know that:
Every internal angle of any rectangle measures 90 degrees, so:
So:
So the measure of angle BEC can be found as follows:
We know that triangle ΔCEB is an isosceles triangle because the diagonals of any rectangle measure the same. So
The sum of internal angles of any triangle add up to 180 degrees, so:
Given:
The given digits are 1,2,3,4,5, and 6.
To find:
The number of 5-digit even numbers that can be formed by using the given digits (if repetition is allowed).
Solution:
To form an even number, we need multiples of 2 at ones place.
In the given digits 2,4,6 are even number. So, the possible ways for the ones place is 3.
We have six given digits and repetition is allowed. So, the number of possible ways for each of the remaining four places is 6.
Total number of ways to form a 5 digit even number is:
Therefore, total 3888 five-digit even numbers can be formed by using the given digits if repetition is allowed.