Question

modeling real life nasas insight is a robotic lander designed to study the deep interior of mars. the solar panels on insight are shaped like regular decagons. find the measure of each interior angle of the solar panels. then find the measure of each exterior angle. interior angle: \\(\square^\circ\\) exterior angle: \\(\square^\circ\\)

Explanation:

Step1: Recall interior angle formula

For a regular $n$-gon, interior angle = $\frac{(n-2)\times180^\circ}{n}$

Step2: Substitute $n=10$ (decagon)

$\frac{(10-2)\times180^\circ}{10} = \frac{8\times180^\circ}{10} = 144^\circ$

Step3: Recall exterior angle property

Sum of exterior angles of any polygon is $360^\circ$. For regular $n$-gon, exterior angle = $\frac{360^\circ}{n}$

Step4: Substitute $n=10$

$\frac{360^\circ}{10} = 36^\circ$

Answer:

Interior angle: $144^\circ$
Exterior angle: $36^\circ$