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Georgia [21]
3 years ago
8

Each interior angle of a regular polygon measures 120°. what is the name of the polygon?

Mathematics
1 answer:
lana66690 [7]3 years ago
4 0
The total angel of any polygons is (n as the totap side of the polygon)
(n - 2) x 180°

now we can substitute 120° into this formula
(n - 2) x 180° / n = 120° (because we're calculating each angle from the polygon, so we need to divide the equation by n)
(180n - 360) = 120n
180n - 120n = 360
60n = 360
n = 6
a 6 side polygon is hexagon.
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Give 1 pair of Vertical and 1 pair of Supplementary angles
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Solution:

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These two angles (140° and 40°) are Supplementary Angles because they add up to 180°:

Notice that together they make a straight angle.

Hence,

From the image

The following pairs form vertical angles

\begin{gathered} \angle1=\angle3(vertical\text{ angles)} \\ \angle2=\angle4(vertical\text{ angles)} \\ \angle5=\angle7(vertical\text{ angles)} \\ \angle6=\angle6(vertical\text{ angles)} \end{gathered}

Hence,

One pair of the vertical angles is ∠1 and ∠3

Part B:

Two angles are said to be supplementary when they ad together to give 180°

Hence,

From the image,

The following pairs are supplementary angles

\begin{gathered} \angle5+\angle6=180^0(supplementary\text{ angles)} \\ \angle5+\angle8=180^0(supplementary\text{ angles)} \\ \angle7+\angle8=180^0(supplementary\text{ angles)} \\ \angle6+\angle7=180^0(supplementary\text{ angles)} \\ \angle1+\angle2=180^0(supplementary\text{ angles)} \\ \angle1+\angle4=180^0(supplementary\text{ angles)} \\ \angle2+\angle3=180^0(supplementary\text{ angles)} \\ \angle3+\angle4=180^0(supplementary\text{ angles)} \end{gathered}

Hence,

One pair of supplementary angles is ∠5 and ∠6

8 0
1 year ago
How to find the measure of angles?
nevsk [136]

Answer:

The best way to measure an angle is to use a protractor. To do this, you'll start by lining up one ray along the 0-degree line on the protractor. Then, line up the vertex with the midpoint of the protractor. Follow the second ray to determine the angle's measurement to the nearest degree.

Step-by-step explanation:

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Answer:

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Answer:

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Step-by-step explanation:

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