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
Karolina [17]
3 years ago
14

Find <ABC. Please help.​

Mathematics
1 answer:
Brilliant_brown [7]3 years ago
6 0

Answer:

\angle\ ABC=70

Step-by-step explanation:

We\ are\ given\ that,\\AB\ and\ AC\ are\ two\ equal\ chords\ on\ the\ circle\ ABC.\\ Let\ the\ center\ of\ the\ circle\ ABC\ be\ O.\\ Angle\ subtended\ at\ the\ Center\ of\ the\ circle\ by\ Chord\ AB\ is\ 110.\\Hence,\\Lets\ connect\ AC\ to\ form\ a\ triangle- \triangle ABC.\\Also,\\O\ forms\ the\ Centroid\ of\ \triangle ABC.

By\ joining\ sides\ AO\ and\ OB,\ we\ obtain\ \triangle ABO.\\Hence,\\\angle BOA=110\ \\Now,\\Considering\ point\ C\ on\ Circle\ ABC,\ lets\ consider\ \angle BCA.

We\ know\ that,\\'Angle\ subtended\ by\ a\ chord\ at\ the\ center\ is\ double\ the\ angle\\ subtended\ by\ the\ same\ chord\ at\ the\ respective\ arc\ of\ the\ circle'.\\Here,\\As\ BOA\ is\ an\ angle\ subtended\ by\ the\ chord\ AB\ at\ the\ center\ of\ circle\ ABC\\ while,\  BCA\ is\ an\ angle\ subtended\ by\ the\ same\ chord\ AB\ at\ the\ major\ arc\ of\\ the\ Circle\ ABC.

Here,\\\angle BOA=2 \angle BCA\\Hence,\\Substituting\ \angle BOA=110,\\110=2*\angle BCA\\Hence,\\\angle BCA=\frac{110}{2}=55

Now,\\We\ also\ know\ that,\\'Base\ angles\ opposite\ to\ equal\ sides\ are\ equal\ too'.\\Here,\\In\ \triangle ABC,\\As\ BA=BC,\\\angle BAC= \angle BCA\\\\\therefore \angle BAC= \angle BCA=55

The\ Angle\ Sum\ Property\ of\ a\ Triangle\ States\ that,\\'The\ Sum\ of\ all\ Interior\ Angles\ of\ a\ Triangle\ is\ 180.'\\Hence,\\As\ Polygon\ ABC\ is\ a\ triangle,\\\angle BCA +\angle BAC +\angle ABC=180\\Substituting\ \angle BCA=\angle BAC=55,\\55+55+ \angle ABC=180\\Hence,\\110+ \angle ABC=180\\Or,\\\angle ABC=180-110=70

You might be interested in
Lakshmi donates 20% of her income to charity. What fraction of her income does Lakshmi donate to charity?
777dan777 [17]

1/5

Hope this helps :)


5 0
3 years ago
A student received a 75% on an exam. If there were 20 questions on the exam, which ratio would show the number of questions answ
Agata [3.3K]
75%=¾
¾*20=15

He answered 15 questions correctly.
6 0
3 years ago
Read 2 more answers
Arthur bought a life insurance policy at $10.98 per month for a 20 year term. What will he pay over 20 years for the premium?
andre [41]
12(months) x 20 (years) = 240

10.98 x 240 = 2635.20

So Arthur will pay $2635.20 over 20 years for premium.

I hope this helps :)
5 0
2 years ago
Read 2 more answers
Solve x/3= 9.<br> 3<br> 12<br> 27<br> 0
MaRussiya [10]
X divided by three equals nine SO to find x you would multiply three times nine
6 0
3 years ago
Read 2 more answers
Convert 120 Ibs to kilograms
posledela

Answer:

54.431 kilograms

Step-by-step explanation:

don't have step by step but 1kg is 2.205lbs

7 0
3 years ago
Other questions:
  • How do you turn .33333333 into a fraction
    5·1 answer
  • 1. Natasha invests £250 in a building society account. At the end of the year her account is credited with 2% interest. How much
    8·1 answer
  • Eight parentheses x plus two parentheses
    9·1 answer
  • Please help do in 10min!!
    11·2 answers
  • 2/3x=10 thankyou for helping me
    8·2 answers
  • There are 600 pages in a novel. Rui feng reads 150 pages of the novel on friday and 40% of the remaining pages on sunday express
    5·1 answer
  • 14. Prove that the number 10^2019 - 1 is composite
    10·1 answer
  • Which two values of x are roots of the polynomial below? <br> 2+5=7
    12·1 answer
  • A car is traveling 40 kilometers per hour. What is the speed of that car in meters per second?
    15·2 answers
  • A student has a rectangular book. The length of the book is 35
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!