Problem 4

x = interior angle
y = exterior angle
x = 3y since "each interior angle...is three times the measure of each exterior angle"

The interior and exterior angles are supplementary, meaning,
x+y = 180
3y+y = 180
4y = 180
y = 180/4
y = 45

So we know that
n = 360/y
n = 360/45
n = 8

You are correct in saying that this is an octagon

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Problem 5

x = measure of missing angles

Find the sum of the interior angles
S = 180*(n-2)
S = 180*(5-2)
S = 540
The five interior angles add up to 540 degrees

Add up the five angles, set equal to 540, then solve for x
90+90+90+x+x = 540
2x+270 = 540
2x+270-270 = 540-270
2x = 270
2x/2 = 270/2
x = 135

So you have the correct answer of choice C) 135 degrees

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Problem 6

S = 180*(n-2)
S = 180*(6-2)
S = 180*4
S = 720

You have the correct answer. Nice work on all three correct answers.

5 0

3 years ago

Write the solution to the given inequality in interval notation.

DIA [1.3K]

Option A: $[4, \infty)$ is the solution

Explanation:

The solution of the given inequality is the set of all the possible values of x.

The graph shows the number line in which the shaded region is from the right of -4 and the arrow of solution goes to infinity.

Also, There is a closed circle at the point -4.

This means that -4 is included in the solution set.

The solution to the inequality is the set of all the real values which are greater than or equal to -4.

Thus, the solution is x ≥ -4

Hence, the solution is $[4, \infty)$

4 0

3 years ago