Question

find the indicated angle measure. 40° a. 100° b. 140° c. 80° d. 20°

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. The central angle corresponding to the $40^{\circ}$ inscribed - angle is $2\times40^{\circ}=80^{\circ}$.

Step2: Use the property of a quadrilateral circumscribing a circle

A quadrilateral circumscribing a circle has the property that the sum of opposite angles is $180^{\circ}$. Let the angle we want to find be $x$. The angle opposite to $x$ in the circum - scribed quadrilateral has a central - angle measure of $80^{\circ}$.
So, $x + 80^{\circ}=180^{\circ}$.

Step3: Solve for $x$

Subtract $80^{\circ}$ from both sides of the equation: $x=180^{\circ}-80^{\circ}=100^{\circ}$.

Answer:

A. $100^{\circ}$