Question

1. the measure of the seven angles in a nonagon measure 138°, 154°, 145°, 132°, 128°, 147°, and 130°. if the two remaining angles are equal in measure, what is the measure of each angle?

Explanation:

Step1: Find sum of interior angles of non - agon

The formula for the sum of interior angles of an $n$-sided polygon is $(n - 2)\times180^{\circ}$. For a non - agon ($n=9$), the sum is $(9 - 2)\times180^{\circ}=7\times180^{\circ}=1260^{\circ}$.

Step2: Calculate sum of given seven angles

$138^{\circ}+154^{\circ}+145^{\circ}+132^{\circ}+128^{\circ}+147^{\circ}+130^{\circ}=974^{\circ}$.

Step3: Let the measure of each of the two equal remaining angles be $x$.

Set up the equation: $974^{\circ}+2x = 1260^{\circ}$.

Step4: Solve for $x$

First, subtract 974 from both sides: $2x=1260^{\circ}-974^{\circ}=286^{\circ}$. Then divide both sides by 2: $x = 143^{\circ}$.

Answer:

$143^{\circ}$