Answer:
49°
Step-by-step explanation:
The given information that BC=DC tells you triangle BCD is an isosceles triangle and that angle y is one of the two equal base angles. Then ...
y + y + 82 = 180 . . . . . the sum of angle measures is 180 degrees
2y = 98 . . . . subtract 82
y = 49 . . . . . divide by 2
The measure of y is 49°.
Okay, so total dogs are 49.
So we know if x=large dogs and y=small dogs, then x+y=49.
Next we are told that there are 36 MORE small dogs than large dogs. We can take that more meaning addition, and x being our value for large dogs. So y=x+36.
After that we now know what value we can plug in for y. So x+x+36=49.
We can then simplify it to 2x+36=49.
Subtracting the 36 from both sides, leaves you with 2x=13.
Followed by dividing both sides by 2, gives you x=6.5. Or 6.5 large dogs.
Now we can plug this into our formula for the small dogs (y=x+36) to give us y=6.5+36, which simplifies to y=42.5. Or 42.5 small dogs. Which is our answer.
We can double check it by adding the small and large dogs together, 6.5+42.5, which gives us 49, our total entries.
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