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 arc - angle relationship

The measure of an inscribed angle is half the measure of its intercepted arc. The sum of the measures of the arcs of a circle is 360°.
Let the measure of arc $\overset{\frown}{EAB}$ be $x$. We know that the sum of the given arcs and the arc we want to find is 360°. The given arcs are 88° and 72°.
The measure of arc $\overset{\frown}{DC}=88^{\circ}$ and assume the measure of arc $\overset{\frown}{EB}$ is $y$.
We know that the sum of the arcs of a circle: $x + 88^{\circ}+y=360^{\circ}$.
Also, using the inscribed - angle property, if we consider the inscribed angles and their intercepted arcs.
The sum of the measures of the arcs of the circle is 360°. We know two arcs: one is 88° and if we assume the other non - relevant arc for now.
We can also use the fact that the sum of the central angles (which is equal to the sum of the arc measures) is 360°.
The measure of arc $\overset{\frown}{EAB}=360^{\circ}-(88^{\circ}+72^{\circ}) = 200^{\circ}$.

Answer:

200°