Question

quadrilateral abcd is inscribed in the circle shown. order the angle - measures from least to greatest.

Explanation:

Step1: Recall property of cyclic quadrilateral

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

Step2: Find $\angle C$

Given $\angle A = 110^{\circ}$, then $\angle C=180 - 110=70^{\circ}$ since $\angle A+\angle C = 180^{\circ}$.

Step3: Find $\angle D$

Given $\angle B = 72^{\circ}$, then $\angle D=180 - 72 = 108^{\circ}$ since $\angle B+\angle D=180^{\circ}$.

Step4: Order the angles

We have $\angle C = 70^{\circ}$, $\angle B=72^{\circ}$, $\angle A = 110^{\circ}$, $\angle D = 108^{\circ}$.
So, the order from least to greatest is $\angle C<\angle B<\angle D<\angle A$.

Answer:

$m\angle C