Question

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

Explanation:

The inscribed - angle theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Here, angle A intercepts arc BCD and angle C intercepts arc BAD. We use this theorem to find the measures of angles A and C in terms of the arc measures.

Answer:

inscribed angle