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
Masteriza [31]
3 years ago
15

In triangle ABC, ∠ABC=70° and ∠ACB=50°. Points M and N lie on sides AB and AC respectively such that ∠MCB=40° and ∠NBC=50°. Find

m∠NMC.

Mathematics
1 answer:
Sever21 [200]3 years ago
3 0

Answer:

∠NMC  = 50°

Step-by-step explanation:

The interpretation of the information given in the question can be seen in the attached images below.

In ΔABC;

∠ A + ∠ B + ∠ C = 180°    (sum of angles in a triangle)

∠ A + 70°  + 50°  = 180°

∠ A = 180° - 70° - 50°

∠ A =  180° - 120°

∠ A =  60°

In ΔAMN ; the base angle are equal , let the base angles be x and y

So; x = y   (base angle of an equilateral  triangle)

Then;

x + x + 60° = 180°

2x +  60° = 180°

2x = 180° - 60°

2x = 120°

x = 120°/2

x = 60°

∴ x = 60° , y = 60°

In ΔBQC

∠a + ∠e + ∠b = 180°

50° + ∠e + 40° = 180°

∠e = 180° - 50° - 40°

∠e = 180° - 90°

∠e = 90°

At point Q , ∠e = ∠f = ∠g = ∠h = 90°  (angles at a point)

∠i  = 50° - 40° = 10°

In ΔNQC

∠f + ∠i   + ∠j = 180°

90° + 10° + ∠j = 180°

∠j  = 180° - 90°-10°

∠j  = 180° - 100°

∠j  = 80°

From  line AC , at point N , ∠y + ∠c + ∠j = 180°   (sum of angles on a straight line)

60° + ∠c + ∠80° = 180°

∠c  = 180° - 60°-80°

∠c  = 180° - 140°

∠c  = 40°

Recall that :

At point Q , ∠e = ∠f = ∠g = ∠h = 90°  (angles at a point)

Then In Δ NMC ;

∠d + ∠h + ∠c = 180°   (sum of angles in a triangle)

∠d + 90° + 40° = 180°

∠d  = 180° - 90° -40°

∠d  = 180° - 130°

∠d  = 50°

Therefore, ∠NMC = ∠d  = 50°

You might be interested in
The value (in degrees) of each of the interior angles of a regular n-gon is represented by x. Write an inequality that describes
Sauron [17]

Answer:

(n - 2)180 = x

3 0
2 years ago
Read 2 more answers
Bonita is testing prototype model rocket engines. To be considered a successful launch, the rocket must reach a height of at lea
galina1969 [7]
(0,33) and (4.8, 30.5) meet our mathematical conditions for this situation. 
3 0
3 years ago
What is the length of leg y of the right triangle?
xz_007 [3.2K]

Answer:

13

Step-by-step explanation:

We need to use the Pythagorean Theorem to solve this problem:

a^{2} +b^{2} = c^{2} , where a and b are the legs of the right triangle and c is the hypotenuse

In this case, we already know b (b = 84) and c (c = 85), so we need to solve for a:

a^{2} = c^{2} - b^{2} = 85^{2} - 84^{2} = 169 = 13^{2}

Thus, a = y = 13.

4 0
3 years ago
Read 2 more answers
7) If you can buy 4 tulip bulbs for $8<br> then how many<br> bulbs can you buy with $32?
Sophie [7]

Answer:

16

Step-by-step explanation:

8/4 = 2  so each bulb costs $2

To find how many bulbs you can buy with $32, divide 32 by 2 = 16

5 0
2 years ago
Read 2 more answers
If the original square had a side length of
irina [24]

Answer:

Part a) The new rectangle labeled in the attached figure N 2

Part b) The diagram of the new rectangle with their areas  in the attached figure N 3, and the trinomial is x^{2} +11x+28

Part c) The area of the second rectangle is 54 in^2

Part d) see the explanation

Step-by-step explanation:

The complete question in the attached figure N 1

Part a) If the original square is shown below with side lengths marked with x, label the second diagram to represent the new rectangle constructed by increasing the sides as described above

we know that

The dimensions of the new rectangle will be

Length=(x+4)\ in

width=(x+7)\ in

The diagram of the new rectangle in the attached figure N 2

Part b) Label each portion of the second diagram with their areas in terms of x (when applicable) State the product of (x+4) and (x+7) as a trinomial

The diagram of the new rectangle with their areas  in the attached figure N 3

we have that

To find out the area of each portion, multiply its length by its width

A1=(x)(x)=x^{2}\ in^2

A2=(4)(x)=4x\ in^2

A3=(x)(7)=7x\ in^2

A4=(4)(7)=28\ in^2

The total area of the second rectangle is the sum of the four areas

A=A1+A2+A3+A4

State the product of (x+4) and (x+7) as a trinomial

(x+4)(x+7)=x^{2}+7x+4x+28=x^{2} +11x+28

Part c) If the original square had a side length of  x = 2 inches, then what is the area of the  second rectangle?

we know that

The area of the second rectangle is equal to

A=A1+A2+A3+A4

For x=2 in

substitute the value of x in the area of each portion

A1=(2)(2)=4\ in^2

A2=(4)(2)=8\ in^2

A3=(2)(7)=14\ in^2

A4=(4)(7)=28\ in^2

A=4+8+14+28

A=54\ in^2

Part d) Verify that the trinomial you found in Part b) has the same value as Part c) for x=2 in

We have that

The trinomial is

A(x)=x^{2} +11x+28

For x=2 in

substitute and solve for A(x)

A(2)=2^{2} +11(2)+28

A(2)=4 +22+28

A(2)=54\ in^2 ----> verified

therefore

The trinomial represent the total area of the second rectangle

7 0
3 years ago
Other questions:
  • The minimum number of carpet rolls n needed to carpet a house varies directly as the house’s square footage h and inversely with
    9·1 answer
  • Meg mixed 1 part of strawberry juice and 3 parts of lemon juice to make lemonade. How many parts of strawberry juice did Meg mix
    15·1 answer
  • The sum of two consecutive integers is less than 83. Find the pair of integers with the greatest sum.
    14·1 answer
  • A grocery store has a shelf with half gallon containers of milk. What type of number best represents the total number of gallons
    6·1 answer
  • How to write 24 min after 2 on the digital clock?? please someone Help me ASAP
    9·2 answers
  • About to submit a topic test, wish me luck!!!
    10·2 answers
  • Help me :&lt;&lt;&lt;&lt;&lt;&lt;&lt;&lt;&lt;&lt;&lt;&lt;_​
    5·1 answer
  • The scale of a map is 1 in.:250 miles. City a is 368 miles from city h. To the nearest tenth, how far is its distance on the map
    6·1 answer
  • Pls help! Solve for p) (p+3)/m = -1
    9·2 answers
  • A muffin recipe calls for 2 eggs to make 12 muffins.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!