Angles in a Pentagon

Substitute and find the total possible angle in a pentagon. There are 5 interior angles in a pentagon. Divide the total possible angle by 5 to determine the value of one interior angle. Each interior angle of a pentagon is degrees. To find the sum of the interior angles of any polygon, use the formula, where n represents the number of sides of a polygon.

The figure above is a pentagon. All of the angles listed except the interior one are exterior angles to the pentagon's interior angles. What is the value of in the figure above? There are two key things for a question like this. The first is to know that a polygon has a total degree measure of:. Next, you should remember that all of the exterior angles listed are supplementary to their correlative interior angles.

This lets you draw the following figure:. Now, you just have to manage your algebra well. You must sum up all what to see in hualien the interior angles and set them equal to. Thus, you can write:. Solve for :. Now, you have to find the largest unknown angle, which is :. In a pentagon, there are 5 sides, or. Substitute and find the total possible angle in a pentagon. There are 5 interior angles in a pentagon. Divide the total possible angle by 5 to determine the value of one interior angle.

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Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney. Hanley Rd, Suite St. Louis, MO Subject optional. Home Embed. Email address: Your name:. Possible Answers:. Correct answer:. Explanation : There are two key things for a question like this.

The first is to know that a polygon has a total degree measure of:where is the number of sides. Therefore, a hexagon like this one has:. This lets you draw the following figure: Now, you just have to manage your algebra well. Thus, you can write: Solve for :. Report an Error. What is the value of the largest unknown angle in the figure above? Thus, you can write: Solve for : Now, you have to find the largest unknown angle, which is :. Explanation : The sum of all angles is determined by the following formula for a polygon: In a pentagon, there are 5 sides, or.

Each interior angle of a pentagon is degrees. The sum of three angles in a pentagon is:. Copyright Notice. Shufang Certified Tutor. Daniel Certified Tutor. Cornell University Alonso Certified Tutor. Report an issue with this question If you've found an issue with this question, please let us know.

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Pentagon is formed from three triangles, so the sum of angles in a pentagon = 3 ? ° Sum of the interior angles of a polygon of n sides = (n – 2) ? ° = °. This makes a condition for the angles of a pentagon as “angle sum property of pentagon”, this helps in solving many problems related to the angles of pentagon. Jun 26, · Now to find the measure of the interior angles of the pentagon, we know that the sum of all the angles in a pentagon is equal to degrees (from the above figure)and there are five angles. (/5 = degrees) So, the measure of the interior angle .

In a five-sided polygon, one angle measures. What are the possible measurements of the other angles? To find the sum of the interior angles of any polygon, use the formula , where n represents the number of sides of a polygon. The sum of the interior angles will be Go through each answer choice and see which one adds up to including the original angle given in the problem.

In a particular heptagon a seven-sided polygon the sum of four equal interior angles, each equal to degrees, is equivalent to the sum of the remaining three interior angles.

Quantity A:. Quantity B:. The sum of interior angles in a heptagon is degrees. Note that to find the sum of interior angles of any polygon, it is given by the formula:. Three interior angles call them are unknown, but we are told that the sum of them is equal to the sum of four other equivalent angles which we'll designate :.

Further more, all of these angles must sum up to degrees:. We may not be able to find , , or , indvidually, but the problem does not call for that, and we need only use their relation to , as stated in the first equation with them. Utilizing this in the second, we find:. What is the value of in the figure above? Always begin working through problems like this by filling in all available information.

We know that we can fill in two of the angles, giving us the following figure:. Now, we know that for any polygon, the total number of degrees in the figure can be calculated by the equation:. Solving for , we get:. Thus, we know for our figure that:. This means that is. Quantity A is larger. If you've found an issue with this question, please let us know.

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Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Hanley Rd, Suite St. Louis, MO Subject optional. Home Embed. Email address: Your name:. Possible Answers:. Correct answer:. Explanation : To find the sum of the interior angles of any polygon, use the formula , where n represents the number of sides of a polygon. In this case: The sum of the interior angles will be The only one that does is , , 95, and the original angle of Report an Error. Example Question 51 : Geometry. Quantity A: Quantity B:.

Possible Answers: Quantity B is greater. Correct answer: Quantity A is greater. Explanation : The sum of interior angles in a heptagon is degrees. Note that to find the sum of interior angles of any polygon, it is given by the formula: degrees, where is the number of sides of the polygon. Three interior angles call them are unknown, but we are told that the sum of them is equal to the sum of four other equivalent angles which we'll designate : Further more, all of these angles must sum up to degrees: We may not be able to find , , or , indvidually, but the problem does not call for that, and we need only use their relation to , as stated in the first equation with them.

Example Question 3 : Pentagons. Explanation : Always begin working through problems like this by filling in all available information.

We know that we can fill in two of the angles, giving us the following figure: Now, we know that for any polygon, the total number of degrees in the figure can be calculated by the equation: , where is the number of sides. Thus, for our figure, we have: Based on this, we know: Simplifying, we get: Solving for , we get: or. Example Question 52 : Geometry.

Quantity A: The measure of the largest angle in the figure above. Possible Answers: The two quantities are equal. Correct answer: Quantity A is larger. Explanation : To begin, recall that the total degrees in any figure can be calculated by: , where represents the total number of sides. Thus, we know for our figure that: Now, based on our figure, we can make the equation: Simplifying, we get: or This means that is.

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