Find the measure of arc QR
A circle with a triangle in it. (10x+10), 7x, (3x-10)
35 degrees
50 degrees
44 degrees
64 degrees
We need more information or a diagram to determine which arc is QR.
To find the measure of arc QR in the circle, we need to use the properties of angles formed by chords in a circle.
We know that the sum of the measures of the angles formed by chords that intersect within a circle is equal to twice the measure of the arc intercepted by the chords.
In this case, we have two chords: (10x+10) and 7x, which intersect at point Q. Let's call the angle formed by these chords at point Q as angle Q.
Since we are trying to find the measure of arc QR, we need to find the measure of angle Q.
Using the property mentioned above, we can set up the following equation:
2 * angle Q = measure of arc QR
Now, let's solve for angle Q:
10x + 10 + 7x = 180 [Sum of angles in a triangle is 180 degrees]
17x + 10 = 180
17x = 180 - 10
17x = 170
x = 170 / 17
x = 10
Now that we know the value of x, we can substitute it back into the expression for angle Q:
angle Q = 10(10) + 10
angle Q = 100 + 10
angle Q = 110 degrees
Finally, we can find the measure of arc QR by multiplying angle Q by 2:
measure of arc QR = 2 * 110 degrees
measure of arc QR = 220 degrees
Therefore, the correct answer is 220 degrees.