• Oct 7th 2007, 03:57 AM

1. How many sides does a regular convex polygon have if the measure of one exterior angle is 2x and the measure of an interior angle is twice that of the exterior angle?

2. Find the measure of the sixth interior angle of a convex hexagon if the sum of the measure of it's five interior angles is 690.

3. The measure of each exterior angle of a regular octagon is 2x-3. Find the value of x and the measure of each exterior angle.

4. Find the measure of the 7th exterior angle a convex heptagon if the sum of the measures of it's six exterior angles is 306.

5. The measures of the interior angles of a polygon are: (y+5) (2y+3) (3y+4) (4y+3) and 5y. What is the value of y? Find the measures of all the interior angles. Give the sum of the measures of all exterior angles.

6. The sum of the measure of three interior angles of a hexagon is 500. Exactly of three remaining angles are complementary and exactly two are supplementary, what are the measures of these three angles?

7. What is the number of sides of a convex polygon if the sum of the measures of its interior angles is between 5800 and 6000?

a. name the polygon according to the number of side it has
b. find the exact sum of the measures of the interior angles
• Oct 7th 2007, 04:09 AM
ticbol
Try posting only one or two Problems per posting and many might help you.

Post a hundred Problems in one posting only and many will think you want them do your homework, and they might not even touch any of your thousand Problems.
• Oct 7th 2007, 04:35 AM
Simplicity
Quote:

3. The measure of each exterior angle of a regular octagon is 2x-3. Find the value of x and the measure of each exterior angle.

3.Every exterior angle on a polygon adds up to 360
°.
$360$
$^{\circ}/8=45^{\circ} \Rightarrow 2x-3=45 \Rightarrow x=24$
• Oct 7th 2007, 04:46 AM
Simplicity
Quote:

2. Find the measure of the sixth interior angle of a convex hexagon if the sum of the measure of it's five interior angles is 690.

4. Find the measure of the 7th exterior angle a convex heptagon if the sum of the measures of it's six exterior angles is 306.

Not sure about the following two answer but I think it may be:

2. $720^{\circ} - 690^{\circ} = 30^{\circ}$

4. $360^{\circ} - 306^{\circ} = 54^{\circ}$

(As: A simple polygon is strictly convex if every internal angle is strictly less than 180 degrees. Equivalently, a polygon is strictly convex if every line segment between two vertices of the polygon is strictly interior to the polygon except at its endpoints. The sum of the interior angles of a regular convex polygon with n sides is equal to 180°(n - 2).)
• Oct 7th 2007, 04:48 AM
Quote:

Originally Posted by ticbol
Try posting only one or two Problems per posting and many might help you.

Post a hundred Problems in one posting only and many will think you want them do your homework, and they might not even touch any of your thousand Problems.

Gomen ne...

>.<

Actually there's 30 problems...:confused:
• Oct 7th 2007, 05:04 AM
Simplicity
Quote:

6. The sum of the measure of three interior angles of a hexagon is 500. Exactly of three remaining angles are complementary and exactly two are supplementary, what are the measures of these three angles?

6. Interior angle in hexagon = 720°
$720^{\circ} - 500^{\circ}= 220^{\circ}$
$220^{\circ} - 90^{\circ} = 130^{\circ}$ --> 130° Is one of the supplementary angle.
$180^{\circ} -130^{\circ} = 50^{\circ}$ --> So the second supplementary angle and the first complementary angle is 50°.
$220^{\circ} - 130^{\circ} - 50^{\circ} = 40^{\circ}$ --> 40° Is the final complementary angle.

Complementary angle add up to 90° --> 50° + 40° =90°
Supplementary angle add up to 180° --> 130° + 50° = 180°
• Oct 7th 2007, 06:22 AM
red_dog
1. Let $\alpha$ be the interior angle and $\beta$ the exterior angle.
We have $\beta =2x, \ \alpha=4x$
$\alpha+\beta=180^{\circ}\Rightarrow x=30^{\circ}\Rightarrow\alpha=120^{\circ}$

Let $n$ be the number of the sides.

$n\alpha=(n-2)180^{\circ}\Rightarrow120^{\circ}n=(n-2)180^{\circ}\Rightarrow n=6$
• Oct 7th 2007, 08:50 AM
Jhevon
Quote:

5. The measures of the interior angles of a polygon are: (y+5) (2y+3) (3y+4) (4y+3) and 5y. What is the value of y? Find the measures of all the interior angles. Give the sum of the measures of all exterior angles.

This page seems to be a very good reference for you, check it out.

we have 5 angles here, so we are dealing with a pentagon.

Now, $\mbox{Sum of Interior Angles } = 180(n - 2)^{\circ}$, where $n$ is the number of sides of the poygon

so here, our interior angles add up to: $180(5 - 2) = 540^{\circ}$

Thus, we must have that:

$(y + 5) + (2y + 3) + (3y + 4) + (4y + 3) + 5y = 540$

solve for $y$ and you can find each angle easily.

for each interior angle, the corresponding exterior angle is given by: $\mbox {Exterior Angle } = 180^{\circe} - \mbox { Interior Angle }$

so that helps you with the second part. good luck
• Oct 7th 2007, 08:57 AM
Jhevon
Quote:

recall that: $\mbox { Sum of Interior Angles } = 180(n - 2)$
thus we want to solve: $5800 \le 180(n - 2) \le 6000$ for $n$. this will help you find the number of sides of the polygon, which makes answering your questions easy. well, the naming question might give you some trouble (see here, problem solved!).