Question

pentagon
number of sides:
sum of interior angles: ____ °
heptagon
number of sides:
sum of interior angles: ____ °
nonagon
number of sides:
sum of interior angles: ____ °
what is the sum of the interior angles of a shape with 100 sides?

Explanation:

for Pentagon:

Step1: Number of sides n=5

Step2: Use formula (n-2)×180°

$(5-2)\times180^\circ$

Step3: Calculate result

$3\times180^\circ=540^\circ$

for Heptagon:

Step1: Number of sides n=7

Step2: Use formula (n-2)×180°

$(7-2)\times180^\circ$

Step3: Calculate result

$5\times180^\circ=900^\circ$

for Nonagon:

Step1: Number of sides n=9

Step2: Use formula (n-2)×180°

$(9-2)\times180^\circ$

Step3: Calculate result

$7\times180^\circ=1260^\circ$

for 100-sided shape:

Step1: Number of sides n=100

Step2: Use formula (n-2)×180°

$(100-2)\times180^\circ$

Step3: Calculate result

$98\times180^\circ=17640^\circ$

Answer:

Pentagon sum of interior angles: 540°
Heptagon sum of interior angles: 900°
Nonagon sum of interior angles: 1260°
100-sided shape sum of interior angles: 17640°