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
Vadim26 [7]
2 years ago
8

In circle D, angle ADC measures (7x + 2)°. Arc AC

Mathematics
1 answer:
Akimi4 [234]2 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 =  m∠ADC

∴ m∠ABC =  × 72

∴ m∠ABC = 36°

You might be interested in
Someone please help me!!
melamori03 [73]

Answer:

All of these questions, I did on paper. Gimme a sec while I upload them

Step-by-step explanation:

6 0
3 years ago
When a number is divided by 5, it has a remainder of 4.
Alexxx [7]

Answer:

37

Step-by-step explanation:

I plugged in the numbers between 35 and 40 and got this. No problem. :)

7 0
2 years ago
How do you know the correct order in which to evaluate algebraic expressions?
GenaCL600 [577]
You should use PEMDAS. I
6 0
2 years ago
You're given two side lengths of 3 centimeters and 5 centimeters. Which measurement can you use for the length of the third side
igomit [66]

Answer: To find the third side of a triangle (there are two answers you could get), you need to use the Pythagorean formula: a^2+b^2=c^2.  First answer, 3^2+5^2=c^2.  Solve for c.  c=5.83.  The second answer, 3^2+b^2=5^2.  Solve for b.  b=4.

\

5 0
3 years ago
Express the distance 48,000,000 meters using scientific notation in meters and then in millimeters
KengaRu [80]

Answer:

Meters:4.8x10 to the 6th power

Millimeters:4.8x 9th power.

Be doin Pearson MathXL

I did 1 today.

8 0
2 years ago
Read 2 more answers
Other questions:
  • Shelly can cut a lawn with a riding mower in 2 hours less time than it takes William to cut the lawn with a push mower. if they
    6·1 answer
  • A bow and arrow cost £22. The bow costs £19 more than the arrow.
    13·1 answer
  • The reciprocal of the cosine is the ___.
    6·2 answers
  • Natalie kicked a soccer ball. The equation h=-16t^2+50t describes the height of the ball (T) seconds after it was kicked. Approx
    7·1 answer
  • Your sock drawer contains 5 pairs of 5 white socks, 3 pair of blue socks, 1 pair of striped socks, and 6 pair of red socks. you
    10·1 answer
  • A man walks for x hours at a speed of
    14·1 answer
  • An express bus and local bus start out at 1rst street together. The express bus stops every 15 blocks. The local bus stops every
    5·1 answer
  • the west valley senior held a fundraiser in which they sold tshirts and hoodies. There were 85 more hoodies sold than tshirts. E
    12·1 answer
  • Triangles XYZ and RST are similar. XY
    13·1 answer
  • The measures of the angles of a triangle are shown in the figure below. Solve for X.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!