1. O is the center of the given circle. The measure of angle O is 134*. The diagram is not drawn to scale.
Assuming that lines that appear to be tangent are tangent, what is the value of X?
A) 67
B) 46
C) 314
D) 268
I've never solved a problem like this without x having a value. Help or the formula to this would help so much, thank you!
To solve this problem, you can use the property that the measure of an angle inscribed in a circle is half the measure of its intercepted arc. Since angle O (134 degrees) is inscribed in the circle, we can find the measure of the arc intercepted by this angle.
To find the measure of the arc intercepted by angle O, we can subtract the measure of angle O from 360 degrees (the total degrees in a circle). Therefore, the intercepted arc measures 360 degrees - 134 degrees = 226 degrees.
Now, since angle O is given as the measure of the central angle, we can calculate the measure of the angle formed by the tangent line and the chord using the formula:
Angle formed by the tangent line and the chord = (1/2) * intercepted arc
Thus, the angle formed by the tangent line and the chord is (1/2) * 226 degrees = 113 degrees.
Next, let's examine the diagram to find x. We can observe that the given angle (113 degrees) is formed between the tangent line and the chord, and x is the measure of the angle formed between the tangent line and the diameter.
Since the diameter of a circle forms a right angle with any tangent line drawn to the circle, and we know that the sum of angles in a triangle is 180 degrees, we can determine the value of x.
We first subtract the given angle (113 degrees) from 180 degrees to find the remaining angle in the triangle:
180 degrees - 113 degrees = 67 degrees.
Therefore, the value of x is 67 degrees.
Hence, the correct option is A) 67.