Question

1. what is the measure of an angle that intercepts a 100 - degree arc in a circle? a. 100 degrees b. 200 degrees c. 50 degrees d. 25 degrees 8. what is the slope of a line that is parallel to the line with the equation y = - 3x+7? a. -1/3 b. 1/3 c. 3 d. -3 9. which of the following is true for any quadrilateral inscribed in a circle? a. opposite angles sum to 180 degrees. b. it is always a rhombus. c. it is always an isosceles trapezoid. d. it is always a rectangle.

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle in a circle is half the measure of the intercepted arc. Given the arc measure is 100 degrees. Let the measure of the inscribed angle be $\theta$. Then $\theta=\frac{1}{2}\times100^{\circ}$.

Step2: Calculate the angle measure

$\theta = 50^{\circ}$

Step3: Recall slope property of parallel lines

The equation of a line is in the form $y = mx + b$, where $m$ is the slope. If two lines are parallel, they have the same slope. The line $y=-3x + 7$ has a slope $m=-3$. So a line parallel to it has a slope of - 3.

Step4: Recall properties of cyclic quadrilaterals

A quadrilateral inscribed in a circle is called a cyclic quadrilateral. The main property of a cyclic quadrilateral is that opposite angles are supplementary, i.e., they sum to 180 degrees.

Answer:

1. C. 50 degrees
2. D. -3
3. A. Opposite angles sum to 180 degrees.