I started a new math class today and I'm stuck on a problem from my worksheet. I need help with these questions.
If the measure of an exterior angle drawn at vertex M of triangle LMN is x, then mangleL + mangleN is what?
What is the area of a circle with the circumference of 18pi centimeteres? Give your answer in terms of pi.
The exterior angle is equal to the sum of the other two interior angles.
C= PI*diameter= PI*radius*2
Area= PI*radius^2= PI (C/2PI)^2= C^2/4PI
check that.
For the first question, you are given that the measure of an exterior angle drawn at vertex M of triangle LMN is x. In a triangle, the sum of the three exterior angles is always 360 degrees. So, if the measure of an exterior angle is x, then the sum of the other two interior angles can be calculated by subtracting x from 360. Therefore, the sum of angle L and angle N is 360 - x.
For the second question, you are given the circumference of a circle which is 18π centimeters. The formula for circumference is C = πd, where d is the diameter of the circle. So, we can rearrange the formula to solve for the diameter:
C = πd
18π = πd
Now, divide both sides by π to solve for the diameter:
d = 18
The diameter is 18 centimeters.
To find the radius (r), we can divide the diameter by 2:
r = d/2
r = 18/2
r = 9
Now, we can use the formula for the area of a circle, which is A = πr^2, to find the area:
A = πr^2
A = π(9)^2
A = π*81
A = 81π
So, the area of the circle is 81π square centimeters.