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
yuradex [85]
3 years ago
6

In triangle ABC, points N and M lie on sides AB and AC, respectively.Given AM = AN = BM = NC = BC, find m∠BAC.

Mathematics
1 answer:
Reil [10]3 years ago
7 0

Answer:

  36°

Step-by-step explanation:

Please refer to the attached figure.

Triangles ANC, AMB, BCN, CBM are all isosceles by virtue of the given congruences. By symmetry, we also claim that ΔABC is isosceles (AB≅AC).

We aren't sure how their internal angles relate, but we can write a couple of equations.

Let x = m∠BAC, y = m∠BCN.

∠NCA = ∠NAC  = ∠MBA = ∠MAB = x

∠BCM = ∠BMC = x +y

∠BMC = ∠MBA +∠MAB = 2x

So, we have ...

  ∠BMC = x +y = 2x   ⇒    y = x

And the sum of angles around ΔABC is ...

  x +(2x) +(2x) = 180°

  x = 180°/5 = 36°

The measure of angle BAC is 36°.

You might be interested in
-9x + 15 = -48 ?????????????????????/
Komok [63]

Answer:

x=7

Step-by-step explanation:

8 0
3 years ago
How to decompose 1 1/6
bearhunter [10]

Answer:

7/6

Step-by-step explanation:

6*1=6

6+1=7

7/6

Hope this helped! :)

3 0
1 year ago
What is the equivalent ratio for6/9
otez555 [7]
The equivalent ration for 6/9 would be 6:9
4 0
3 years ago
If Emily has 6 apples and she give hailey 2 apples how many apples does she have in all
vladimir1956 [14]

Answer:

6? ........m...........

5 0
3 years ago
Please help marking brainliest if correct!!
BlackZzzverrR [31]

Answer:

Step-by-step explanation:

2x=5x+60.

0=3x+60 ( subtract 2x from both sides)

-60=3x(subtract 60 on both sides)

x=-20

Hope this helps plz mark brainliest if correct :D

6 0
3 years ago
Read 2 more answers
Other questions:
  • Can someone please help me with this?
    14·1 answer
  • What is the value of 28
    13·1 answer
  • Please help. I have been stuck for days now
    7·1 answer
  • Simplify the following expression.
    13·1 answer
  • (3,7)(2,6) Find the equation for the line that falls through the two ordered pairs
    15·1 answer
  • Find the value of x!!!!
    12·1 answer
  • Sarah is training for a bike race. She rides her bike 5 3/4 miles in 1/3 hour. What is Sarah’s rate in miles per hour. Express y
    10·2 answers
  • What is the x-intercept of the graph 0f 27= -3x2?
    8·1 answer
  • Rewrite (3x + 2)(x - 3) in standard form
    12·1 answer
  • Question 9/30 If ADD = 81, BAD = 49, and CAD = 64. then what is the value of ADA?​
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!