Arc AB measures 5x + 2. Angle ACB measures 3x + 14. Find the value of x.
Angles and arcs have different dimensions. Both are presented as dimensionless numbers in your question.
The question makes no sense to me.
Presumably C is the center of a circle, and A and B are points on the circle.
arc AB = r * angle ACB
5x+2 = r(3x+14)
5x+2 = 3rx + 14r
x(5-3r) = 14r-2
x = (14r-2)/(5-3r)
Not knowing the radius of the circle, it's tough to get a value for x.
Angle C is an inscribed angle of circle P. Angle C measures (3x + 6)° and arc AB measures (8x)°. Find x.
To find the value of x, we need to use the information given about the arc AB and the angle ACB.
Arc AB is measured by 5x + 2.
Angle ACB is measured by 3x + 14.
Since ACB is an angle formed by intersecting arcs AB and AC, we can set up an equation to find the value of x.
According to the properties of circles, the measure of an angle formed by intersecting arcs is equal to half the sum of the arcs' measures. In this case, angle ACB is formed by arcs AB and AC.
So, we can write the equation as follows:
3x + 14 = (1/2)(5x + 2)
To solve for x, we will distribute the 1/2 to the terms inside the parentheses:
3x + 14 = (5/2)x + 1
Next, we can isolate x by moving the terms involving x to one side of the equation:
3x - (5/2)x = 1 - 14
Combining like terms:
(6/2)x - (5/2)x = -13
Simplifying:
(1/2)x = -13
To solve for x, we will multiply both sides of the equation by 2:
2 * (1/2)x = 2 * -13
x = -26
Therefore, the value of x is -26.