The measure of 13 of the 14 angles of a 14-gon add up to 2016 what must be the 14th angle measure be

There is a way to solve for the interior angles of the polygon add up to, by using the expression: (Note: n being the side:  (n - 2)180

solve for the 14 angles first. Plug in 14 for n

14 - 2 = 12

12 x 180 = 2160

All of the angles combined together = 2160°. Note that it is given to us that 13 of the angles = 2016°

Solve for the last angle. Set the last (14th) angle as x:

x + 2016 = 2160.

Isolate the x. Note the equal sign, what you do to one side, you do to the other. Subtract 2016 from both sides

x + 2016 (-2016) = 2160 (-2016)

x = 2160 - 2016

x = 144

The 14th angle must be 144°

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Hi there! To solve this problem you must start by finding the sum of the measures of the interior angles in the 14-gon.

We can do this easily by using the formula for the sum pf the measures of the interior angles in a polygon if we have the number of sides (14).

The formula is: (n - 2) * 180, where n represents the number of sides in the polygon that you are trying to solve for.

Since we are trying to solve for the measures of the angles of a 14-gon, then substitute in 14 for n in the formula and evaluate the expression.

((14) - 2) * 180

By the law of pemdas, you must solve inside the parentheses first and then multiply the answer you get by 180.

(12) * 180

Now you can multiply 12 by 180 to find the sum of the measures of the interior angles of the 14-gon.

12 * 180 = 2,160

Now that we know this, we can make the 14th angle equal the variable "x", and use the sum of the other 13 angles (2,016) as the other term in the equation.

The variable x (14th angle) and 2,016 (other 13 angles) will add up to equal 2,160 (the sum of all the angles). The equation should look like:

(x) + (2,016) = 2,160

You can remove the parentheses as they aren't really needed, they are just to show the addition of the two expressions. The equation should look like:

x + 2,016 = 2,160

To solve this equation, you first need to move all terms containing the variable you are trying to solve for on the left side of the equation and all other terms to the right side of the equation.

This means that you need to subtract 2,016 from both sides of the equation. Now your equation should look like:

x = 144

Since the variable x represented the measure of the 14th angle in this 14-gon, that means that the measure of the 14th angle in this 14-gon is 144 degrees.

Your answer is: The 14th angle measure is 144 degrees.

Hope this helped you-- have a great day! Comment below if you have further questions.

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9