Question

let the measure of $overparen{bcd} = a^{circ}$. because $overparen{bcd}$ and $overparen{bad}$ form a circle, and a circle measures $360^{circ}$, the measure of $overparen{bad}$ is $360 - a^{circ}$. because of the ________ theorem, $mangle a = \frac{a}{2}$ degrees and $mangle c = \frac{360 - a}{2}$ degrees. the sum of the measures of angles a and c is $left( \frac{a}{2} + \frac{360 - a}{2}
ight)$ degrees, which is equal to $\frac{360^{circ}}{2}$, or $180^{circ}$. therefore, angles a and c are supplementary because their measures add up to $180^{circ}$. angles b and d are supplementary because the sum of the measures of the angles in a quadrilateral is $360^{circ}$. $mangle a + mangle c + mangle b + mangle d = 360^{circ}$, and using substitution, $180^{circ} + mangle b + mangle d = 360^{circ}$, so $mangle b + mangle d = 180^{circ}$.what is the missing information in the paragraph proof?$circ$ inscribed angle$circ$ polygon interior angle sum$circ$ quadrilateral angle sum$circ$ angle bisector

Explanation:

The proof relates the measure of an inscribed angle (angles A and C) to half the measure of its intercepted arc ($\overset{\frown}{BCD}$ and $\overset{\frown}{BAD}$ respectively). This relationship is defined by the inscribed angle theorem, which states that an inscribed angle is half the measure of its intercepted arc. The other options do not describe this arc-angle relationship: polygon interior angle sum and quadrilateral angle sum refer to total interior angles of shapes, while angle bisector involves splitting an angle into two equal parts.

Answer:

A. inscribed angle