Question

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

Explanation:

Step1: Recall the sum of arc - measures in a circle

The sum of the measures of the arcs of a circle is 360°.

Step2: Identify the given arc - measures

We are given that one arc has a measure of 88° and another has a measure of 130° and 70°. Let the measure of arc $\overline{EAB}$ be $x$.

Step3: Set up an equation

$x + 88^{\circ}=360^{\circ}-(130^{\circ}+70^{\circ})$

Step4: Simplify the right - hand side of the equation

First, calculate the sum inside the parentheses: $130^{\circ}+70^{\circ}=200^{\circ}$. Then, $360^{\circ}-200^{\circ}=160^{\circ}$. So, $x + 88^{\circ}=160^{\circ}$.

Step5: Solve for $x$

Subtract 88° from both sides of the equation: $x=160^{\circ}-88^{\circ}=72^{\circ}$.

Answer:

$72^{\circ}$