Ashley is building a picture frame for a gift. the frame will be a hexagon with equal angles, pieced together with six individual wood boards. Determine the angle should Ashley cut the boards to complete the project.
To determine the angle Ashley should cut the boards, we need to divide the total sum of the interior angles of a hexagon equally among the six boards.
The formula to calculate the sum of the interior angles of a polygon is given by:
Sum of interior angles = (n - 2) * 180 degrees
where n is the number of sides of the polygon. In this case, as the frame is a hexagon (a polygon with six sides), we can substitute n = 6 into the formula:
Sum of interior angles = (6 - 2) * 180 degrees
Sum of interior angles = 4 * 180 degrees
Sum of interior angles = 720 degrees
Now, since the hexagon is made up of six equal angles, we divide the sum of the interior angles by 6 to find the measure of each angle:
Measure of each angle = Sum of interior angles / Number of angles
Measure of each angle = 720 degrees / 6
Measure of each angle = 120 degrees
Therefore, Ashley should cut the boards at a 120-degree angle to complete the hexagonal picture frame.
Ashley is building a picture frame for a gift. the frame will be a hexagon with equal 60 degree angles, pieced together with six individual wood boards. Determine the angle should Ashley cut the boards to complete the project.
If the angles of the hexagon are equal and each angle measures 60 degrees, this means that the boards need to be cut at half the angle of the hexagon's interior angle in order to fit together properly.
The interior angle of a hexagon is given by the formula:
Interior angle = (n - 2) * 180 degrees / n
where n is the number of sides of the polygon. In this case, as the frame is a hexagon, n = 6. Plugging this into the formula, we get:
Interior angle = (6 - 2) * 180 degrees / 6
Interior angle = 4 * 180 degrees / 6
Interior angle = 720 degrees / 6
Interior angle = 120 degrees
Since the boards need to be cut at half the angle of the hexagon's interior angle, Ashley should cut the boards at an angle of 120 degrees / 2 = 60 degrees in order to complete the hexagonal picture frame.
in triangle PQR, QR = 7.2m, PQ = 8.8m and <P = 35 degree, sketch the triangle then use the Sine Law to determine the measure of <R the nearest degree.
To determine the measure of angle R using the Sine Law, we need to use the following ratio:
sin(R) / PQ = sin(P) / QR
Given that PQ = 8.8m, QR = 7.2m, and <P = 35 degrees, we can substitute the values and solve for sin(R):
sin(R) / 8.8m = sin(35 degrees) / 7.2m
To find sin(R), multiply both sides of the equation by 8.8:
sin(R) = (sin(35 degrees) / 7.2m) * 8.8m
sin(R) = sin(35 degrees) * (8.8m / 7.2m)
sin(R) = sin(35 degrees) * (1.22)
Using a calculator to find sin(35 degrees), we get:
sin(R) = 0.5736 * 1.22
sin(R) = 0.7005
Now, to find the measure of angle R, we need to take the inverse sine (sin^(-1)) of 0.7005:
R = sin^(-1)(0.7005)
Using a calculator, we find:
R ≈ 44.5 degrees
Therefore, angle R of triangle PQR measures approximately 44.5 degrees (to the nearest degree).
To determine the angle that Ashley should cut the boards for the hexagonal picture frame, we can use the fact that the sum of the interior angles of a hexagon is 720 degrees. Since the hexagon has equal angles, we divide 720 degrees by 6 (the number of angles) to find the measure of each angle.
720 degrees ÷ 6 = 120 degrees
Therefore, Ashley should cut the boards at a 120-degree angle to complete the project.
To determine the angle at which Ashley should cut the boards for the hexagonal picture frame, we need to know that the sum of the interior angles in a polygon is given by the formula:
Sum of interior angles = (n - 2) * 180 degrees
In this case, Ashley is constructing a hexagon, which has six sides. Therefore, we can substitute n = 6 into the formula:
Sum of interior angles = (6 - 2) * 180 degrees
Sum of interior angles = 4 * 180 degrees
Sum of interior angles = 720 degrees
Since all angles of a hexagon are equal, we can divide the sum of the angles by the number of angles to find the measure of each angle:
Each angle of the hexagon = 720 degrees / 6
Each angle of the hexagon = 120 degrees
So, Ashley should cut the boards at an angle of 120 degrees to complete the hexagonal picture frame.