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
Alex_Xolod [135]
3 years ago
12

In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE║ AB. Find the measures of the angles of ΔABC, if m∠ADE: m∠ADB = 2

:9.

Mathematics
1 answer:
drek231 [11]3 years ago
6 0

Answer:   ∠A=48°,∠B=48°,∠C=84°.


Step by-step explanation:

Given:  AD and BE are the angle bisectors  of ∠A and ∠B

i.e ∠6=∠7    ( ∵ Angles formed after  AD bisected ∠A)

∠4=∠5       ( ∵ Angles formed after  BE bisected ∠B)

Also,  DE║AB

⇒ ∠2=∠7   (∵ Alternate interior angles)

   ∠3=∠6   (∵ Alternate interior angles)

And ∠ADE : ∠ADB =∠2:∠3= 2:9 =2x : 9x     ..(1)

To Find:  ∠A,∠B,∠C.

Solution:  ∠2=∠7 (∵ Given)    ...(2)

∠2=∠4  (∵ angles on the same segment)    ...(3)

∠4=∠5 =∠B/2 (∵ Given)    ...(4)

∴ In Δ ABD

∠3+∠4+∠5+∠7 = 180 (∵ Sum of interior angles of a triangle)

From equation 2,3,4,5, Put values

9x+2x+2x+2x =180°

⇒15x = 180°

⇒x=12°

Putting values in equation (4) ⇒ ∠ B =2*(2*12) = 48°

Also, <u>∠B=∠A=48°</u>

Now,in Δ ABC

∠C+∠B+∠A= 180°

⇒48°+48°+∠C= 180°

<u><em>⇒∠C=84°</em></u>

You might be interested in
What is the slope of the line y = -5x +1 ?
laila [671]

Answer:

-5

Step-by-step explanation:

Remember the slope intercept form:

y = mx + b

m = Slope value

b = y-intercept

So in this case,

y = (-5)x + b

m = -5

b = 1

Thus the answer is -5

3 0
3 years ago
What steps do I take for this
Luden [163]
First, divide the shape into two figures ( a semicircle and a rectangle)
Then, find the are or the two shapes using the area formula for a semicircle (\frac{ \pi r^{2} }{2}) and the are formula for a rectangle (base x height)
Finally, add the two areas together and you have your answer

7 0
3 years ago
Mishka is on a long road trip, and she averages 75 mph for 2 hours while she's driving on the highway. While she's driving on si
slega [8]

If she goes 75 mph for 2 hours, that's 150 miles altogether. 45 mph for 1 hour is 45 miles, so 150 + 45 is 195 miles.

8 0
3 years ago
IS IT A OR B PLEASE ANSWER FOR BRAINLIEST!!!
maks197457 [2]
I say the answer is A, correct me if I'm wrong.
5 0
3 years ago
What is the quotient of -3/8 and -1/3 <br> O -1 1/8<br> O -1/8<br> O 1/8<br> O 1 1/8
Nat2105 [25]
The quotient of -3/8 and -1/3 is 1 1/8.
3 0
3 years ago
Other questions:
  • Write two expressions where the solution is 28
    10·1 answer
  • What is the probability that the code number for a new customer will begin with a 7
    15·1 answer
  • A) Explain...
    9·1 answer
  • Please explain your answer
    14·1 answer
  • Can someone please help me? thanks!
    15·2 answers
  • Helppp !!!! .......................................................................
    13·1 answer
  • This is an isosceles trapezoid.<br> R.<br> s<br> 75<br> X<br> Y У<br> T<br> U
    9·2 answers
  • 3<br>An aeroplane flies 4200 km at a speed of 800 km/ how long is the flight​
    7·1 answer
  • 1. Jillian Knits hats for her family and friends. In the week, she knits 4 hats, the next week, she has some help and together,
    5·1 answer
  • (x+y)^2 expressions that are equivalent
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!