Question

quadrilateral abcd is inscribed in the circle shown. order the angle - measures from least to greatest. m∠b m∠c m∠d m∠a

Explanation:

Step1: Recall property of cyclic quadrilateral

In a cyclic quadrilateral, opposite angles are supplementary, i.e., $\angle A+\angle C = 180^{\circ}$ and $\angle B+\angle D=180^{\circ}$. Given $\angle A = 108^{\circ}$, then $\angle C=180 - 108=72^{\circ}$. Given $\angle B = 72^{\circ}$, then $\angle D=180 - 72 = 108^{\circ}$.

Step2: Compare angle - measures

We have $\angle A = 108^{\circ}$, $\angle B = 72^{\circ}$, $\angle C = 72^{\circ}$, $\angle D = 108^{\circ}$. Arranging from least to greatest: $\angle B=\angle C<\angle A=\angle D$.

Answer:

$m\angle B=m\angle C < m\angle A=m\angle D$