2. Using the external angle of a triangle theorem.
6x - 17 = 3x - 11 + 2x + 11
6x - 5x = 17
x = 17
So m angle K = 2(17) + 11
= 45 degrees answer
3. The diagonals are both medians of the triangle so the 2 parts are in the ratio 2:1 so 3:x = 2:1 and x = 1.5 answer
2:1
Since he sells 5 large cards for every 2 small, we can multiply the number of small cards he needs to sell by 2.5 to find how many large cards he needs to sell.
So let x=the number of small cards sold, and 2.5x=the number of large cards sold
The equation is:Total profit=x+(2.5x)
Since a small card is $2.5, a large card is $4, and the total profit will be $10,000 plug those in to make the equation:
10,000=2.5x+4(2.5x)
We can combine the x's to get 10,000=12.5x and then divide both sides by 12.5 to get x=800.
So he needs to sell 800 small cards.
Multiply that by that 2.5.
And he needs to sell 2000 large cards.
