What is the measure of 1

Chase is building a birdhouse in the shape of a regular polygon. He knows that the measure of the interior angle is twice the me

mel-nik [20]

Answer:

The perimeter of the base of the birdhouse is 36 units

Step-by-step explanation:

<u><em>The complete question is</em></u>

Chase is building a birdhouse in the shape of a regular polygon. He knows that the measure of the interior angle is twice the measure of the exterior angle and the length of a diagonal that passes through the center is 12. What is the perimeter of the base of the birdhouse?

step 1

Find the measure of the interior angle

Let

x ---> the measure of the interior angle

y ---> the measure of the exterior angle

Remember that

the sum of the interior and exterior angle in any polygon is equal to 180 degrees

so

$x+y=180^o$ ----> equation A

we have that

the measure of the interior angle is twice the measure of the exterior angle

so

$x=2y$ ----> equation B

substitute equation B in equation A

$2y+y=180$

$y=60^o$

so

$x=120^o$

That means-----> The figure is a regular hexagon

step 2

Remember that

The length of the diagonal that passes through the center of the hexagon is equal to two times the length of the regular hexagon

Let

b ----> the length side of the hexagon

so

$b=12/2=6\ units$

The perimeter of the hexagon is given by the formula

$P=6b$

substitute

$P=6(6)=36\ units$

3 0

3 years ago

Help! What’s the measure of angle RST? Please explain, I want to learn.

KatRina [158]

The angle where the letter S is which would be angle RSQ = 1/2 x (131 +43) = 87

the angle opposite os RSQ would be PST and that would equal the same as RSQ which is 87

so 2 angles = 87 +87 = 174

so the other 2 angles need to equal 360 - 174 = 186

since opposite angles equal each other divide that by 2 so 186 / 2 = 93

so both angle RST and PSQ are 93

The answer is D 93 degrees

4 0

3 years ago

Read 2 more answers

In a group of 21 students, 8 students take Art courses, 7 students take Music courses. Two students take both courses. A student

Blababa [14]

Since two people take both courses, we can subtract two from 7, 8, and 21, giving us 5, 6, and 19.

Add 5 and 6 together to get 11. Since eleven students are in those two groups, we can answer this. The answer will be 11/19.

3 0

3 years ago

Given the data shown below, which of the following is the best approximation of the coefficient of determination (r^2)

HACTEHA [7]

The coefficient of determination can be found using the following formula:

$r^2=\mleft(\frac{n(\sum ^{}_{}xy)-(\sum ^{}_{}x)(\sum ^{}_{}y)}{\sqrt[]{(n\sum ^{}_{}x^2-(\sum ^{}_{}x)^2)(n\sum ^{}_{}y^2-(\sum ^{}_{}y)^2}^{}}\mright)^2$

Using a Statistics calculator or an online tool to work with the data we were given, we get

So the best aproximation of r² is 0.861

8 0

1 year ago

Determine whether the relation is a function. -8, 0 -1, 5 4,10,11

11111nata11111 [884]

Vas happenin!

It’s a function because the Xs don’t repeat

Hope this helps

-Zayn Malik

6 0

3 years ago