# 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]

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]

## This Post Has 10 Comments

1. alexabbarker9781 says:

:0000000000000000000000

2. annie8348 says:

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

3. sony72 says:

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)

13.9 units

4. Jaaaack says:

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 :

$Area =\frac{5}{2}\times side\times apothem\\\\\implies Area=\frac{5}{2}\times 14.1\times 9.7\\\\\implies Area = 341.925\: cm^2\\\\\implies Area\approx 341.9\:cm^2$

Therefore, The required area of the regular pentagon = 341.9 cm²

Hence, The correct option is C. 341.9 cm²

5. EllaSue says:

6. rickyg1354 says:

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.

7. johndacres8280 says:

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°

8. Lovebamagirl12 says:

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

9. YmTia06221220 says:

12.9

Step-by-step explanation:

AB = $\sqrt{2^{2}+3^{2} }$ = $\sqrt{13}$

BC = $\sqrt{2^{2}+2^{2} }$ = $2\sqrt{2}$

CD = $\sqrt{1^{2}+2^{2} }$ = $\sqrt{5}$

DE = 3

EA = $\sqrt{1^{2} + 2^{2} }$ = $\sqrt{5}$

The sum of all of these (in decimal form) is (approx.) 12.9

10. Mendi1026 says:

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.