Question

what is the measure of eab in circle f? 72° 148° 92° 200°

Explanation:

Step1: Recall the property of a cyclic - quadrilateral

The sum of opposite angles in a cyclic - quadrilateral is 180°. In cyclic - quadrilateral EBCD, ∠E + ∠C=180°. Given ∠E = 70°, then ∠C = 110°.

Step2: Use the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Let the measure of arc EAB be \(x\) and the measure of arc EDB be \(y\). The sum of the measures of the arcs of a circle is 360°, so \(x + y=360^{\circ}\). Also, the inscribed angle ∠C intercepts arc EDB, so \(y = 2\angle C=220^{\circ}\).

Step3: Solve for the measure of arc EAB

Since \(x + y=360^{\circ}\) and \(y = 220^{\circ}\), then \(x=360^{\circ}-y\). Substituting \(y = 220^{\circ}\) into the equation, we get \(x = 140^{\circ}\). However, we made a wrong start above.
Let's use another approach.
The sum of the interior angles of a quadrilateral is 360°. In quadrilateral EABC, we know two angles ∠E = 70° and ∠B = 80°.
The measure of the arc intercepted by an inscribed angle is twice the measure of the inscribed angle.
The measure of arc EDB is \(2\times\angle C\). First, find ∠C using the angle - sum property of[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]

Answer:

Step1: Recall the property of a cyclic - quadrilateral

The sum of opposite angles in a cyclic - quadrilateral is 180°. In cyclic - quadrilateral EBCD, ∠E + ∠C=180°. Given ∠E = 70°, then ∠C = 110°.

Step2: Use the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Let the measure of arc EAB be \(x\) and the measure of arc EDB be \(y\). The sum of the measures of the arcs of a circle is 360°, so \(x + y=360^{\circ}\). Also, the inscribed angle ∠C intercepts arc EDB, so \(y = 2\angle C=220^{\circ}\).

Step3: Solve for the measure of arc EAB

Since \(x + y=360^{\circ}\) and \(y = 220^{\circ}\), then \(x=360^{\circ}-y\). Substituting \(y = 220^{\circ}\) into the equation, we get \(x = 140^{\circ}\). However, we made a wrong start above.
Let's use another approach.
The sum of the interior angles of a quadrilateral is 360°. In quadrilateral EABC, we know two angles ∠E = 70° and ∠B = 80°.
The measure of the arc intercepted by an inscribed angle is twice the measure of the inscribed angle.
The measure of arc EDB is \(2\times\angle C\). First, find ∠C using the angle - sum property of[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]