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

Explanation:

Step1: Recall the sum of angles in a cyclic - quadrilateral

The sum of opposite angles in a cyclic quadrilateral is 180°. In cyclic quadrilateral EBCD, ∠E + ∠C = 180° and ∠B+∠D = 180°.

Step2: Find the measure of arc EAB

The measure of an arc is related to the inscribed - angle subtended by it. The sum of the measures of the arcs of a circle is 360°. The measure of arc DCB = 88° + 80°=168°. We know that the measure of an inscribed angle is half the measure of the intercepted arc. Let the measure of arc EAB be (x). The sum of the measures of the major and minor arcs of a circle is 360°. So, (x+168^{\circ}=360^{\circ}).

Step3: Solve for (x)

Subtract 168° from both sides of the equation (x + 168^{\circ}=360^{\circ}). (x=360^{\circ}-168^{\circ}=192^{\circ}). But this is wrong. Let's use another approach. The sum of the interior angles of the cyclic - quadrilateral EBCD: ∠E = 70°, ∠B = 80°, ∠C and ∠D are given as parts of arc - related angles. The measure of arc EAB: We know that the sum of the measures of the arcs of a circle is 360°. The measure of arc DC = 88° and arc CB = 80°. The measure of arc EAB=360°-(88° + 80°)=192° (wrong approach). The correct way: The sum of the angles in the cyclic - quadrilateral EBCD: ∠E = 70°, ∠B = 80°, ∠D = 88°. Let's use the property that the sum of the angles in a cyclic - quadrilateral is 360°. First, find ∠C. ∠E+∠B + ∠C+∠D=360°. So, ∠C=360°-(70° + 80°+88°)=122°. The measure of arc EAB: The measure of an arc is twice the measure of the inscribed angle subtended by its non - intercepted arc. The inscribed angle ∠C subtends arc EAD. The measure of arc EAB = 2(∠C + ∠D). ∠C = 122° and ∠D = 88°. The measure of arc EAB=200°.

Answer:

200°