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
Stella [2.4K]
3 years ago
7

AB is tangent to the circle k(O) at B, and AD is a secant, which goes through center O. Point O is between A and D∈k(O). Find m∠

BAD and m∠ADB, if the measure of arc BD is 110°20'.

Mathematics
2 answers:
drek231 [11]3 years ago
5 0

Answer:

∠BAD=20°20'

∠ADB=34°90'

Step-by-step explanation:

AB is tangent to the circle k(O), then AB⊥BO. If the measure of arc BD is 110°20', then central angle ∠BOD=110°20'.

Consider isosceles triangle BOD (BO=OD=radius of the circle). Angles adjacent to the base BD are equal, so ∠DBO=∠BDO. The sum of all triangle's angles is 180°, thus

∠BOD+∠BDO+∠DBO=180°

∠BDO+∠DBO=180°-110°20'=69°80'

∠BDO=∠DBO=34°90'

So ∠ADB=34°90'

Angles BOD and BOA are supplementary (add up to 180°), so

∠BOA=180°-110°20'=69°80'

In right triangle ABO,

∠ABO+∠BOA+∠OAB=180°

90°+69°80'+∠OAB=180°

∠OAB=180°-90°-69°80'

∠OAB=20°20'

So, ∠BAD=20°20'

Sergeu [11.5K]3 years ago
4 0

Answer:

The measure of ∠BAD and ∠ADB is 20°20' and 34°90' respectively.

Step-by-step explanation:

Given that AB is tangent to the circle k(O) at B, and AD is a secant, which goes through center O. Point O is between A and D∈k(O).

measure of arc BD is 110°20'.

we have to find the measure of ∠BAD and ∠ADB

∠4=110°22'

In ΔOBD, by angle sum property of triangle

∠1+∠2+∠4=180°

∠1+∠2+110°20'=180°

∠1+∠2=69°80'

Since OB=OD(both radii of same circle) therefore ∠1=∠2

2\angle 2=69^{\circ}80'

\angle 2=\frac{69^{\circ}80'}{2}=34^{\circ}90'

m∠ADB=34°90'

As OB is radius of circle and AB is tangent therefore by theorem which states that radius is perpendicular on the tangent line gives

\angle 6=90^{\circ}

By exterior angle property

∠5=∠1+∠2=69°80'

By angle sum property in ΔABO

∠3+∠6+∠5=180°

∠3+90°+69°80'=180°

∠3=20°20'

You might be interested in
In a race, 41 out of the 50 bicyclists finished in less than 38 minutes. What percent of bicyclists finished the race in less th
storchak [24]
For left put 2 on each
On the box over 100 put 82, and put 82 in the box on the right
5 0
2 years ago
Read 2 more answers
What is the answer to <br>-5+62×(-2)?
ladessa [460]
-129 is the anwser to ur problem
3 0
3 years ago
Read 2 more answers
Please help me out man<br><br> f/ 6 = 17
ratelena [41]

Answer:

f/6=17

f=17×6

=102

Hope it helps!!!

7 0
2 years ago
Read 2 more answers
I honestly don't know how I got these answers and I have a test over it coming soon. Please explain how to find the measure of t
Tju [1.3M]
Okay so a couple of things to know to best solve this problem
1) all angles in a triangle add to 180
2) a straight line the angles above it equal 180 and the angles below it add to 180
3) vertical angles are equal (vertical angles are angles that make an X the opposite angles are called vertical angles)
5 0
3 years ago
Read 2 more answers
A middle school has 600 students and 34% of them are in the 8th grade. One-fourth of 8th graders walk to school. How many 8th gr
Kaylis [27]

600 * .34 =  204 are in 8th grade

204 * 1/4 = 51 51 8th graders walk to school

D

5 0
2 years ago
Read 2 more answers
Other questions:
  • A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random
    14·1 answer
  • Is 2xy = -8 a function
    15·2 answers
  • Can somebody help me with this it a little hard
    5·1 answer
  • On Monday, Jayla raised $30 and Carlos raised $50.
    6·1 answer
  • The equation of the horizontal line passing through the point (-3, 8) is y = 8. O True O False​
    12·2 answers
  • I have a brain and I know most of you are using brainly to cheat in school
    15·1 answer
  • Carla used 6 1/2 cups of sugar to make five pies. How many cups of sugar will she need to make 2 pies?​
    14·1 answer
  • Which one is right for this please
    15·1 answer
  • -1 1/3 + 3/4<br> Plz help me I am doing a test and I really need the answer!!!!
    6·2 answers
  • A circle has a radius of 6 yards. A sector of the circle that is 12. 56 yards² is painted. What is the angle measurement of the
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!