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]
4 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]4 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
I NEED HELP‼️
Ivenika [448]

Answer:

All but the second one

Step-by-step explanation:

The rule of a function is that you can't have the same x values in an expression. You can have multiple y values but not multiple x values.

6 0
3 years ago
What is the range of g(x)?
Jlenok [28]

Answer:

The function g(x) is defined for all real numbers x. The maximum value of the range is 4. The maximum value of the domain is 3. The range of g(x) is {y| –1 < y ≤ 4}.

Step-by-step explanation:

i don't know what your question is exactly but hope this helps.

8 0
3 years ago
If I have more 15 Pokemon cards than Austin, which expression shows how many |<br>have?​
Nataly_w [17]

Answer:

a+15=x

Step-by-step explanation:

Austin is represented as variable a, and you have 15 more cards.

x is your amount of cards

5 0
2 years ago
What is the sum of 3 + (-4) ?
andreev551 [17]

Answer:-1

Step-by-step explanation:3-4=-1

5 0
3 years ago
Read 2 more answers
The absolute value of -5 is...
ipn [44]

Answer:

The absolute value of -5 is...5

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • Shauna borrows $400 from her parents to buy a phone. She agrees to pay them back plus 4% simple interest over one year. Part A W
    15·1 answer
  • 3) The coordinates of point A are (−3, 6) and the coordinates of point B are (3, −6). Find the slope of AB
    10·2 answers
  • What is the area of the figure?
    14·1 answer
  • Please help!<br>What is the answer to this question?<br>​
    10·2 answers
  • Use logarithm table to solve (0.7634)^4​
    5·1 answer
  • Please help me, i will give brainiest !!
    6·2 answers
  • Fill in the missing numbers to complete the linear equation that gives the rule for this table.
    10·1 answer
  • Please help me solve for x
    10·1 answer
  • When positive integer x is divided by positive integer y, the remainder is 9. If = 96.12, what is the value of y ? 96 75 48 25 1
    7·1 answer
  • Let’s apply this understanding to situations when we’re given the context and function.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!