can someone please answer these questions for me?:
1. if the measure of an interior angle of a regular pentagonis 108 degrees, then the angle sum of that regular pentagon must be:
A. 120 degrees
B. 360 degrees
C. 540 degrees
D. 720 degrees
2. is it possible for a parallelogram to have a 38 degree angle and a 145 degree angle? explain please
3. a rectangle has a perimeter of 24 centimeters. one of its sides is 8 centimeters long. what are the dimensions of the rectangle? explain please
4. is it possible for a triangle to have angles with measures of 40 degrees, 115 degrees and 30 degrees? please explain
thanks :D sorry if theres soo many questions, i just really need help
sum of interior angles = 180(n-2) where n is the number of sides
so each angle is 180(n-2)/n
180(n-2)/n = 108
180n - 360 = 108n
72n = 360
n = 5
So you have a pentagon
angle sum = 180(5-2) = 540
do the others the same way.
Remember in #2, that n has to be a whole number.
(e.g. A pentagon cannot have 4.3 sides)
#3. Just think about it again.
you have one of the sides.
How does one find the perimeter?
1. The angle sum of a regular pentagon can be found by multiplying the number of sides by the interior angle. Since a regular pentagon has 5 sides, and the interior angle is given as 108 degrees, the angle sum is 5 * 108 = 540 degrees. Therefore, the answer is C. 540 degrees.
2. In a parallelogram, opposite angles are congruent, meaning they have the same measure. If the given angles are 38 degrees and 145 degrees, they are not opposite angles. Therefore, it is not possible for a parallelogram to have angles of 38 degrees and 145 degrees.
3. The perimeter of a rectangle is the sum of all its sides. Let's denote the length of the rectangle as L and the width as W. The perimeter is given as 24 centimeters, which can be written as 2L + 2W. One of the sides is given as 8 centimeters, so we can write the equation as 2L + 2(8) = 24. Simplifying this equation, we get 2L + 16 = 24. Subtracting 16 from both sides, we get 2L = 8. Dividing by 2, we find L = 4. So, one side is 8 centimeters long (given) and the other side (the width) is 4 centimeters long. Therefore, the dimensions of the rectangle are 8 centimeters by 4 centimeters.
4. The sum of the angles in any triangle is always 180 degrees. If the angles of a triangle are given as 40 degrees, 115 degrees, and 30 degrees, let's check if their sum is 180 degrees. Adding these angles together, we have 40 + 115 + 30 = 185 degrees. Since the sum is not equal to 180 degrees, it is not possible for a triangle to have angles with measures of 40 degrees, 115 degrees, and 30 degrees.
Sure, I'm here to help! Let's go through each question step by step:
1. To find the angle sum of a regular pentagon, we need to know the number of sides. In a regular polygon, each interior angle is the same. Since the given angle is 108 degrees, we can determine the number of sides by dividing 360 degrees (the angle sum of any polygon) by 108 degrees. So, 360/108 = 3.33. Since we can't have a fraction of sides, the closest whole number is 3. Therefore, the regular pentagon in question does not exist as a 3-sided polygon. None of the answer choices are correct.
2. In a parallelogram, opposite angles are congruent (or equal). If one angle is 38 degrees, the opposite angle must also be 38 degrees. Similarly, if one angle is 145 degrees, the opposite angle must also be 145 degrees. Since the opposite angles in a parallelogram are not congruent in this case, it is not possible for a parallelogram to have a 38 degree angle and a 145 degree angle.
3. The perimeter of a rectangle is the sum of all its sides. Let's call the length of the rectangle L and the width W. Given that one side is 8 centimeters long, we can create an equation for the perimeter: 2L + 2W = 24. We can also substitute one of the variables since we know that L = 8. Plugging this into the equation, we have 2(8) + 2W = 24, which simplifies to 16 + 2W = 24. Subtracting 16 from both sides gives us 2W = 8, and then dividing both sides by 2, we find W = 4. Therefore, the dimensions of the rectangle are 8 centimeters by 4 centimeters.
4. In a triangle, the sum of all three angles must be 180 degrees. Let's add up the angles: 40 + 115 + 30 = 185. Since the sum is greater than 180 degrees, it is not possible for a triangle to have angles with measures of 40 degrees, 115 degrees, and 30 degrees.
I hope that helps! Let me know if you have any further questions.