Question

what is the measure of arc 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 BCDE, ∠B + ∠D=180° and ∠E + ∠C = 180°.

Step2: Find the measure of arc EDB

The measure of an inscribed angle is half the measure of its intercepted arc. The inscribed angle ∠E = 70°, so the measure of arc DCB is 2×70° = 140°. Given arc DC = 88°, then arc CB=140° - 88° = 52°.

Step3: Find the measure of arc EAB

The sum of the measures of the arcs of a circle is 360°. Arc EDB= arc ED+ arc DC + arc CB. Arc ED is not given directly, but we know that the inscribed - angle relationships. The measure of arc EAB=360°-(88° + 52°)=220°. However, if we assume there is a mistake in the above - mentioned approach and use the fact that for an inscribed angle ∠B = 80°, the measure of arc EDC is 2×80° = 160°. Since arc DC = 88°, arc ED=160° - 88° = 72°. Then the measure of arc EAB=360°-(72° + 88°)=200°.

Answer:

200°