1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anvisha [2.4K]
2 years ago
5

Points E, F, and D are on circle C, and angle G measures 60°. The measure of arc EF equals the measure of arc FD.

Mathematics
2 answers:
galben [10]2 years ago
5 0

Answer:

∠EFD ≅ ∠EGD ⇒ A

Arc ED ≅ arc FD ⇒ C

m arc FD = 120° ⇒ E

Step-by-step explanation:

Let us revise some facts

  1. Equal chords subtended equal arcs
  2. The measure of an inscribed angle is one-half the measure of the central angle which subtended by the same arc
  3. The measure of a central angle is equal to the measure of its subtended arc
  4. If one angle of an isosceles triangle measure 60° then the triangle is equilateral
  5. The sum of the measures of the interior angles of any quadrilateral is 360°

In the quadrilateral  CDGE

∵ m∠G = 60°

∵ m∠GDC = m∠GEC = 90°

- By using the 5th rule above

∴ m∠G + m∠GDC + m∠DCE + m∠GEC = 360°

∴ 60 + 90 + m∠DCE + 90 = 360

∴ 240 + m∠DCE = 360

- Subtract 240 from both sides

∵ m∠DCE = 120°

In circle C

∵ ∠DCE is a central angle subtended by arc DE

∵ ∠DFE is an inscribed angle subtended by arc DE

- By using the 2nd rule above

∴ m∠DFE = \frac{1}{2} m∠∠DCE

∵ m∠DCE = 120°

∴ m∠DFE = \frac{1}{2} (120)

∴ m∠DFE = 60°

- That means ∠EFD ≅ ∠EGD because their measure is 60°

∴ ∠EFD ≅ ∠EGD

In Δ EFD

∵ EF = FD

∵ m∠DFE = 60°

- By using the 4th rule above

∴ Δ EFD is an equilateral triangle

∴ ED = FD = FE

In circle C

∵ Side ED subtended by arc ED

∵ Side FD subtended by FD

∵ Side ED ≅ side FD ⇒ proved

- By using the 1st rule above

∴ Arc ED ≅ arc FD

∵ m∠ECD = 120°

∵ ∠ECD is a central angle subtended by arc ED

- By using the 3rd rule above

∴ m∠ECD = m arc ED

∴ m of arc ED = 120°

∵ Arc ED ≅ arc FD

∴ m arc ED = m arc FD

∴ m arc FD = 120°

marta [7]2 years ago
5 0

Answer:

A, C, and D

Step-by-step explanation:

Right on Edge

You might be interested in
Is s = 2 a solution to the inequality below?<br><br> 32<br> s<br> &gt; 19<br> Yes Or no
erica [24]

Answer:

YES

Step-by-step explanation:

32(2)>19

64>19

TRUE

7 0
3 years ago
Simplify the following to an expression involving a single<br> trig function with no fractions.
Verizon [17]

Answer    

Step-by-step explanation:

cos x

4 0
3 years ago
Hhhhhhhhhhhhhhhhhhhhhhhhheeeeeeeeeeeeeeeeeeellllllllllllllllllllllllllllppppppppppppppppp
VikaD [51]

Answer:

Jeandre is correct, and they are 2 units from zero

Step-by-step explanation:

The absolute value of 2 is 2, and the absolute value of -2 is 2. Absolute value is the real number without a sign. If you put both 2s, on the number line, they would be the same length from zero. Hope this helps!

4 0
3 years ago
Read 2 more answers
The triangular prism has a volume of 27 cubic units.
Neporo4naja [7]

Answer:

1 cubic unit will be the volume of the prism.

Step-by-step explanation:

Volume of the triangular prism = 27 cubic units

Since formula of volume of the triangular prism = (1/3)A×h

27 = (1/3)A×h ⇒ Ah = 27×3 = 81

Now each side of the prism is dilated then we have to calculate the volume of new prism.

V' = (1/3)×A'×h'

= (1/3) (1/9)A×(1/3)h = (1/81)×Ah = (1/81)×81 = 1 cubic unit

Therefore the volume of new prism will be 1 cubic unit

7 0
3 years ago
Read 2 more answers
What is the value of k?<br> L<br> k=<br> 8.<br> m<br> O<br> 4<br> k<br> N<br> 1<br> M
AleksAgata [21]

Answer:

i think its 8

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • Factor y2 + 10z - 10y - yz
    11·2 answers
  • B. How many adults are needed if there
    14·2 answers
  • 4 sisters love barrettes. they have a value pack that contains 92 barrettes. how many barrettes can each sister have if they sha
    10·2 answers
  • What is 56 times 67899
    6·1 answer
  • Alanna is painting a border on a wall. The border consists of kite-shaped figures as shown.
    7·2 answers
  • Dude is making 12 pounds of nut mixture with macadamia nuts and almonds. Macadamia nuts cost $9 per pound and almonds cost $5.25
    8·1 answer
  • What shape is in the interior of these four<br> lines? Classify it.
    10·1 answer
  • Please hurry
    9·1 answer
  • Том и Эми установили будильники на своих телефонах на 6:45. Оба сигнала тревоги звучат одновременно в 6.45. Будильник Тома звучи
    7·1 answer
  • Please help!!!!!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!