Answer:
z = 110
Step-by-step explanation:
The measure of an angle created by the intersection of two secants outside a circle is half the difference of the angles it intercepts. In this it would be:
2x + 15 = 1/2 * (10x + 20 - 80)
We can now solve:
4x + 30 = 10x - 60
30 = 6x - 60
6x = 90
x = 15
This means the values of 10x + 20 is 10(15) + 20, which is 170.
Now, we can add up all the arcs in a circle, which sum to 360 degrees:
360 = z + 170 + 80
360 = z + 250
z = 110
A-1500
B-1500
C-1500+1500=3000
Because base angles are congruent, both angle A and B are congruent. If the two triangles are congruent, then the base angles are the same, meaning 5x=50*. Divide by 10 and you get the answer of x=5. :) Hope this helps!
Answer:
A
Step-by-step explanation:
given 2 secants drawn from an external point to the circle , then
the product of the measures of one secant's external part and that entire secant is equal to the product of the other secant's external part and that entire secant, that is
9(9 + 2 + 3x) = 10(10 + 2x + 2)
9(11 + 3x) = 10(12 + 2x) ← distribute parenthesis on both sides
99 + 27x = 120 + 20x ( subtract 20x from both sides )
99 + 7x = 120 ( subtract 99 from both sides )
7x = 21 ( divide both sides by 7 )
x = 3
I kind-of need more specifics here. You didn't give any dimensions, but okay. So if you notice, from the side, any cone just looks like a regular old triangle. And we can treat it like one when trying to find the slant height. Ever heard of the Pythagorean theorem? a squared plus b squared = c squared. so in this case, the hypotenuse, or c-side, will be your slant height. take the square of the distance from the circle-base's center to the apex. add that to the square of the radius of the base. Find the square root (using your calculator) of that sum, and there's your answer.
