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4 years ago

Find the sum of the measures of the interior angles of apolygon with 10 sides.

Mathematics

1 answer:

motikmotik4 years ago

3 0

Answer:

1440

Step-by-step explanation:

The sum of the exterior angles of a regular polygon of 10 sides = 360 deg. The sum of the interior angles of a regular polygon of 10 sides = 10*[180 - (360/10)] = 10(180–36) = 10*144 = 1440 deg.

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In ∆ABC, m∠A = 60º, m∠C = 30º, and AB = 6 inches. What is the length of side BC?

Alex17521 [72]

The length of the side BC is 6√3 inches

Step-by-step explanation:

Let us revise the sine rule

In Δ XYZ

The side XY is opposite to angle Z
The side YZ is opposite to angle X
The side XZ is opposite to angle Y
The sine rule is $\frac{XY}{sin(Z)}=\frac{YZ}{sin(X)}=\frac{XZ}{sin(Y)}$

In Δ ABC

∵ m∠A = 60°

∵ m∠C = 30°

∵ AB = 6 inches

- By using the sine rule

∵ AB is opposite to ∠C

∵ BC is opposite to ∠A

∵ $\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

∴ $\frac{6}{sin(30)}=\frac{BC}{sin(60)}$

- By using cross multiplication

∴ BC × sin(30) = 6 × sin(60)

∵ sin(30) = $\frac{1}{2}$ and sin(60) = $\frac{\sqrt{3}}{2}$

∴ $\frac{1}{2}$ BC = 6( $\frac{\sqrt{3}}{2}$ )

∴ $\frac{1}{2}$ BC = $3\sqrt{3}$

- Multiply both sides by 2

∴ BC = 6√3

The length of the side BC is 6√3 inches

Learn more:

You can learn more about the triangles in brainly.com/question/1238144

#LearnwithBrainly

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3 years ago

Lucy started to run on a treadmill after setting its timer for 77 minutes. The display says that she has finished 79% of her run

max2010maxim [7]

Answer:

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Step-by-step explanation:

Step 1: Go on g oogle

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Find the sum of the measures of the interior angles of apolygon with 10 sides.​

Find the sum of the measures of the interior angles of apolygon with 10 sides.