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]
3 years ago
8

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

Mathematics
1 answer:
viktelen [127]3 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
The pair of points (g, -1) and (2, 5) lie on a line with a slope of 3/2. What is the value of g?
Sliva [168]

Answer:

\huge{ \boxed{ \bold{g =  - 2}}}

Step-by-step explanation:

In order to find g we have to use the formula for finding the slope of the line passing through two points that's

m =  \frac{y_2 -y_ 1}{x_2 -x_1 }  \\

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are (g, -1) and (2, 5) and m = 3/2

We substitute it into the equation and find g

That's

\frac{3}{2}  =  \frac{5 -  - 1}{2 - g}  \\  \frac{3}{2}  =  \frac{5 + 1}{2 - g }  \:  \:  \:  \:  \:  \:  \:  \frac{3}{2}  =  \frac{6}{2 - g}  \\  \\ 3(2 - g) = 6(2) \\ 6 - 3g = 12 \\  - 3g = 12 - 6 \\  - 3g = 6 \\  \\  \frac{ - 3g}{ - 3}  =  \frac{6}{ - 3}  \\  \\ g =  - 2

We have the final answer as

<h3>g = - 2</h3>

Hope this helps you

7 0
1 year ago
Please help, awarding brainliest and extra points
Svet_ta [14]

Answer:

to get that just divied i wanna say

Step-by-step explanation:

3 0
2 years ago
Andrew lives at an altitude of 135 feet, and his friend Lisa lives at an altitude of -10 feet. blank residence is higher than bl
tatiyna

Answer:

Andrews residence is higher than Lisa's residence

Step-by-step explanation:


6 0
3 years ago
Read 2 more answers
This so fking confusing
love history [14]

Answer:

m

Step-by-step explanation:

m

8 0
3 years ago
Read 2 more answers
What is the slope of (4,1) and (6,-1)
schepotkina [342]

Answer:

slope = -1

Step-by-step explanation:

you <u>subtract the y-values</u> (-1-1=-2) then <u>subtract the x-values</u> (6-4=2) then divide the sum of the y-values by the sum of the x-values

\frac{-2}{2} which simplifies to a slope of -1

6 0
2 years ago
Other questions:
  • In California, state sales tax rates vary by county. In Alameda County, the sales tax rate is 8 1/2%.
    10·1 answer
  • Pls can someone help me on this thank you
    15·3 answers
  • Write an inequality that represents this situation
    11·1 answer
  • Steve's doctor has advised him to take protein supplements. He bought two brands, Brand A and Brand B. The table gives the amoun
    12·1 answer
  • Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k.
    5·2 answers
  • Catherine and Lance open a savings account at the same time. Catherine deposits $100 initially and adds $20 per week. Lance depo
    15·2 answers
  • Which of the following lengths of lines could be used to create a right triangle
    11·2 answers
  • Can you help me with Maths? =)
    8·1 answer
  • Add 10ft 3in + 3ft 9in + 8ft 10in​
    13·1 answer
  • If there are 3 black t-shirts, 2 white t-shirts, and 5 green t-shirts, What is the probability of picking white?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!