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
Katarina [22]
3 years ago
13

In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°. Circle D is shown. Points A, B, and C are on the circle. P

oint C is on the opposite side of points A and C. LInes are drawn from point A to point B, from point B to point C, from point C to point D, and from point D to point A. Angle A D C measures (7 x + 2) degrees. Arc A C measures (8 x minus 8) degrees. What is the measure of Angle A B C ? 36° 43° 72° 144°
Mathematics
2 answers:
olchik [2.2K]3 years ago
8 0

Answer:

36

Step-by-step explanation:

Juli2301 [7.4K]3 years ago
7 0

Answer:

The measure of angle ABC is 36° ⇒ 1st answer

Step-by-step explanation:

Let us revise some important facts in the circle

  • The measure of the center angle is equal to the measure of its subtended arc
  • The measure of the inscribed angle is equal to half the measure of the central angle subtended by the same arc
  • The vertex of a central angle is the center of the circle and its sides are radii in the circle
  • The vertex of an inscribed angle is a point on the circle, and its sides are chords in the circle

In circle D

∵ D is the center of the circle

∵ A and C lie on the circle

- DA and DC are radii

∴ ∠ADC is a central angle subtended by arc AC

∴ m∠ADC = m of arc AC

∵ m∠ADC = (7x + 2)°

∵ m of arc AC = (8x - 8)°

- Equate them to find x

∴ 8x - 8 = 7x + 2

- subtract 7x from both sides

∴ x - 8 = 2

- Add 8 to both sides

∴ x = 10

Substitute the value of x in the measure of ∠ADC

∵ m∠ADC = 7(10) + 2 = 70 + 2

∴ m∠ADC = 72°

∵ AB and BC are two chords in circle D

∴ ∠ABC is an inscribed angle subtended by arc AC

∵ ∠ADC is a central angle subtended by arc AC

- By using the 2nd fact above

∴ m∠ABC = \frac{1}{2} m∠ADC

∴ m∠ABC = \frac{1}{2} × 72

∴ m∠ABC = 36°

You might be interested in
ASAP I need help 10 points
schepotkina [342]

Answer: Mitzi can buy 8 pounds of strawberries.

Step-by-step explanation:

when you divide 6 by 0.75 you get 8. So your answer is 8 pounds.

7 0
3 years ago
Solve the equation on the interval [0,2pi] 5sec(x)+7=-3
vovangra [49]

Answer:

Hello,

x\in \bigg\{\dfrac{2\pi}{3} ,\dfrac{4\pi}{3}\bigg\}\\

Step-by-step explanation:

5*sec(x)+7=-3\\\\sec(x)=\dfrac{-10}{5} \\\\\dfrac{1}{cos(x)} =-2\\\\cos(x)=-\dfrac{1}{2} \\\\x=120^o\ or\ x=240^o\\

8 0
2 years ago
Read 2 more answers
How do you solve this?
Katarina [22]

\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] ~\dotfill\\\\ (x-6)^2+(y+5)^2=16\implies [x-\stackrel{h}{6}]^2+[y-(\stackrel{k}{-5})]^2=\stackrel{r}{4^2}~\hfill \begin{cases} \stackrel{center}{(6,-5)}\\ \stackrel{radius}{4} \end{cases}

Check the picture below.

6 0
3 years ago
Read 2 more answers
Help ASAP !’please explain
patriot [66]

Answer:

First one is 15.Second one is 3

Step-by-step explanation:

1 inch:10 meters 150÷10:15 26÷2:13 6÷2:3

4 0
3 years ago
Find the unknown. 531 = ( × 6) + 21
sladkih [1.3K]
The answer would be x = 85
3 0
3 years ago
Read 2 more answers
Other questions:
  • In the given figure, values of x and y, are 1. 40°, 25° 2. 30°, 40° 3. 30°, 20° 4. 40°, 35°
    10·1 answer
  • What is the standard equation for a circle with the center (2,1) and passing through (0, 1)
    13·2 answers
  • Number 35 plz and thank you ☺️ worth 25 points
    15·2 answers
  • Simplify the following expression 19-(-8)-(-4)
    15·1 answer
  • What is an equation of the line that passes through the point (-3, -7) and is
    6·1 answer
  • The difference between two numbers is 3. Their sum if 27. What is the smaller number?
    9·2 answers
  • If AC = 14, what is the measure of AD? Round your answer to the nearest hundredth.
    15·1 answer
  • Mrs. Wilson bought 2 gallons of bubbles to pour into “bubble containers” as party favors. If she pours ⅛ of a gallon into each “
    13·1 answer
  • Which expression is equivalent to 3/ x^5y ?
    10·1 answer
  • Ahmed says that 0.505005000500005 is a rational number because it is a repeating decimal, is he correct? Explain your reasoning.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!