Point C is the center of the circle. If angle ACB measures 4 x plus 12 degrees and AB measures x plus 13 degrees, find x.
what is AB? the angle subtending the arc AB? If so, then it is also angle ACB, so
4x+12 = x+13
x = 1/3
butt math sucks who agree's
To find the value of x, we can use the properties of angles in a circle:
1. In a circle, the measure of an angle formed by a chord is half the sum of the measures of the intercepted arcs.
2. The arc intercepted by angle ACB is arc AB.
Given that angle ACB measures 4x + 12 degrees and arc AB measures x + 13 degrees, we can set up the equation:
4x + 12 = 2(x + 13)
Simplifying the equation:
4x + 12 = 2x + 26
Subtracting 2x from both sides:
2x + 12 = 26
Subtracting 12 from both sides:
2x = 14
Dividing both sides by 2:
x = 7
Hence, the value of x is 7.