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
Furkat [3]
2 years ago
8

O is the centre of the circle. AB is a diameter.

Mathematics
1 answer:
viktelen [127]2 years ago
3 0

Answer:

The value of a is 63° and the value of b is 27°

Step-by-step explanation:

In the given figure

∵ OA, OB, and OC are radii of the circle O

→ The radii of a circle are equal

∴ OA = OB = OC

In Δ AOC

∵ OA = OC

∴ Δ AOC is an isosceles triangle

→ Base angles of the isosceles triangle are equal

∵ ∠OAC and ∠OCA are the base angles of the triangle

∴ m∠OAC = m∠OCA

∵ m∠OAC = a°

∴ m∠OCA = a°

→ The sum of angles in any triangle is 180°

∵ a° + a° + m∠AOC = 180°

∵ m∠AOC = 54°

∴ a° + a° + 54 = 180°

→ Add the like terms

∴ 2a° + 54 = 180°

→ Subtract 54 from both sides

∴ 2a° = 126°

→ Divide both sides by 2

∵ m∠OAC = m∠OCA = 126 ÷ 2

∴ a° = 63

∴ The value of a is 63°

In ΔBOC

∵ OB = OC

∴ Δ BOC is an isosceles triangle

→ Base angles of the isosceles triangle are equal

∵ ∠OBC and ∠OCB are the base angles of the triangle

∴ m∠OBC = m∠OCB

∵ m∠OBC = b°

∴ m∠OCB = b°

∵ ∠AOC is an exterior angle of ΔBOC at the vertex O

→ The measure of the exterior angle equals the sum of the measure

    of the opposite interior angles to this vertex

∵ ∠OBC and ∠OCB are the opposite interior angle of ∠AOC

∴ m∠OBC + m∠OCB = m∠AOC

→ Substitute their measures

∵ b° + b° = 54°

→ Add the like terms

∴ 2b° = 54

→ Divide both sides by 2

∴ b° = 27

∴ The value of b is 27°

You might be interested in
Which are correct representations of the inequality -3(2x - 5) <5(2-x)? Select two options.
antoniya [11.8K]

Answer:

what? I don't get

Step-by-step explanation:

4 0
3 years ago
Answer this pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeee I will mark brainliest​
Anna [14]

Answer:

the answer is B

Step-by-step explanation:

it is B cause the line is going up so it is a positive linear function and the more he studies the higher he gets on his test

4 0
2 years ago
Put 4,685÷3 in long division only exceptions for pictures of it solved
cricket20 [7]
The answer is 1561r2
8 0
2 years ago
Identify the common factor of 16,24,50
goldenfox [79]
The common factor is 2
5 0
3 years ago
Read 2 more answers
Find the value of x.<br> 89"<br> (6x + 5)"
vivado [14]
The value of x is 14
(6x+5)=89–>89-5 = 84 —> 84/6=14 —> x=14
6 0
3 years ago
Other questions:
  • Which one of the following proportions is true for the segments shown in the figure if lines a, b, and c are parallel to each ot
    12·1 answer
  • Given x less than y, compare the following expressions and determine which is greater: 2x-y;2y-x. Explain your answer
    12·1 answer
  • Plzzz helppppp. 4&gt;n/-4
    7·2 answers
  • Solve x + x + 2 + 2x = -2.
    6·2 answers
  • What value of x will make this expression equal to 28.1? A) x=0 is the only value that will make the expression equal to 28.1 B)
    6·1 answer
  • Help me plz thank u so much
    11·1 answer
  • What is the solution to 34x + 95 = 3 (14X +9)
    15·2 answers
  • Plss help meeeeeeeeeeeeeeee
    12·2 answers
  • Convert 1100111 into decimal numbers ​
    14·1 answer
  • Hat is the measure of the unknown angle?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!