Answer:
Measure of 7 angles is 144 degrees each and measure of 8th angle is 72 degrees.
Step-by-step explanation:
An octagon is an 8-sided polygon. We are given that 7 angles of the octagon have the same measure while one angle is 1/2 times (i.e. half of the other angles). So if each of the 7 angles measure x degrees, the measure of 8th angles would be x/2 degrees.
The sum of internal angles of a polygon can be calculated as:
180(n-2), where n is the number of sides of the polygon. So for an octagon n=8, therefore the sum of internal angles of octagon would be:
180(8-2)= 180 x 6 = 1080 degrees.
We can write the equation as:
Sum of internal angles of octagon = 1080
[tex]7x + \frac{x}{2} = 1080\\\\\frac{15x}{2}=1080\\\\15x=2160\\\\ x=144[/tex]
This means, 7 of the angles measure 144 degrees and one angle measures 144/2 = 72 degrees.
