N the diagram below, points $A,$ $E,$ and $F$ lie on the same line. If $ABCDE$ is a regular pentagon, and $\angle EFD=90^\circ$, then how many degrees are in the measure of $\angle FDE$? [asy]
size(5.5cm);
pair cis(real magni, real argu) { return (magni*cos(argu*pi/180),magni*sin(a rgu*pi/180)); }
pair a=cis(1,144); pair b=cis(1,72); pair c=cis(1,0); pair d=cis(1,288); pair e=cis(1,216);
pair f=e-(0,2*sin(pi/5)*sin(pi/10));
dot(a); dot(b); dot(c); dot(d); dot(e); dot(f);
label("$A$",a, WNW);
label("$B$",b, ENE);
label("$C$",c, E);
label("$D$",d, ESE);
label("$E$",e, W);
label("$F$",f, WSW);
draw(d--f--a--b--c--d--e);
draw(f+(0,0.1)--f+(0.1,0.1)--f+(0.1 ,0));
[/asy]
:0000000000000000000000
108 degrees
Step-by-step explanation:
angle CDE is 108 degrees, which is supplementary to angle EDH, so EDH must be 72 degrees
then put it into an equation
90+90+72+x=360
solve
x=108
13.9 units
Step-by-step explanation:
AB = sqrt(2² + 3²) = sqrt(13)
BC = sqrt(2² + 2² = sqrt(8)
CD = sqrt(1² + 2²) = sqrt(5)
DE = 3
EA = sqrt(1² + 2²) = sqrt(5)
Add all these:
13.9 units
The correct option is C. 341.9 cm²
Step-by-step explanation:
Length of the apothem is given to be 9.7 cm
Also, Side length of the regular pentagon is given to be 14.1 cm
Now, we need to find the area of the pentagon :
So, Area of the regular pentagon is given by the formula :
[tex]Area =\frac{5}{2}\times side\times apothem\\\\\implies Area=\frac{5}{2}\times 14.1\times 9.7\\\\\implies Area = 341.925\: cm^2\\\\\implies Area\approx 341.9\:cm^2[/tex]
Therefore, The required area of the regular pentagon = 341.9 cm²
Hence, The correct option is C. 341.9 cm²
The answer is 108
Step-by-step explanation:
1. Connect points E and T, then B and T.
2. 10 triangles would be congruent to ATB
3. The questions is bad. Right triangles are defined as angles, and the other two are side descriptions. The triangle being drawn would be a 30-60-90 triangle, which is a right scalene triangle.
4. 30 degrees.
5. 60 degrees.
The measure of ∠FDE = 18°
Explanation:
A Pentagon has 5 sides and is made of 3 triangles
So, sum of the interior angles of the triangle = 180°
Therefore, the total interior angle of a regular pentagon = 3 X 180° = 540°
A regular pentagon will have all its angle equal
All the five angles would make 540°
Let the measure of one angle = x
So,
5x = 540°
x = 108°
Therefore, the measure of each angle of a pentagon is 108°
From the diagram,
∠AED + ∠FED = 180°
∠AED = 108° as it is one of the sides of the pentagon
So,
108° + ∠FED = 180°
∠FED = 72°
In ΔEFD,
∠FED + ∠EFD + ∠FDE = 180°
72° + 90° + ∠FDE = 180°
∠FDE = 18°
Therefore, the measure of ∠FDE = 18°
Correct option: fourth one -> 10 units
Step-by-step explanation:
As the pentagon is regular, all the sides have the same length, so we just need to find the length of the side AE and then multiply by 5.
To find the length of AE we can find the distance from point A to point E:
distance from A to E:
sqrt( (4-2)^2 + (1-1)^2) = 2 units
To the perimeter of the pentagon is 5 * 2 = 10 units.
Correct option: fourth one
12.9
Step-by-step explanation:
AB = [tex]\sqrt{2^{2}+3^{2} }[/tex] = [tex]\sqrt{13}[/tex]
BC = [tex]\sqrt{2^{2}+2^{2} }[/tex] = [tex]2\sqrt{2}[/tex]
CD = [tex]\sqrt{1^{2}+2^{2} }[/tex] = [tex]\sqrt{5}[/tex]
DE = 3
EA = [tex]\sqrt{1^{2} + 2^{2} }[/tex] = [tex]\sqrt{5}[/tex]
The sum of all of these (in decimal form) is (approx.) 12.9
Angle x = 108 degrees
Step-by-step explanation:
Find the total angle degree of a pentagon: (n-2)x180
(5-2)x180 = 3x180 = 540
So, 540 degrees is the total degree measure.
540/5 to find the interior degree of angle x. Since it's a regular pentagon, all interior angles have the same measure.
540/5=108
Therefore, 108 degrees is the size of angle x.