which statement is true regarding the diagram of circle p? the sum of y and z must be 2x. the sum of y and z…

which statement is true regarding the diagram of circle p? the sum of y and z must be 2x. the sum of y and z must be $\frac{1}{2}x$. the difference of z and y must be 2x. the difference of z and y must be $\frac{1}{2}x$.

which statement is true regarding the diagram of circle p? the sum of y and z must be 2x. the sum of y and z must be $\frac{1}{2}x$. the difference of z and y must be 2x. the difference of z and y must be $\frac{1}{2}x$.

Answer

Explanation:

Step1: Recall the angle - measure formula for angles formed by two secants

The measure of an angle formed by two secants of a circle is given by the formula $x=\frac{1}{2}(z - y)$, where $x$ is the measure of the angle formed by the two secants outside the circle, $z$ is the measure of the larger intercepted arc, and $y$ is the measure of the smaller intercepted arc.

Step2: Rearrange the formula

Multiply both sides of the equation $x=\frac{1}{2}(z - y)$ by 2. We get $2x=z - y$.

Answer:

The difference of $z$ and $y$ must be $2x$.