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
alexgriva [62]
3 years ago
10

In a rectangle MPKN, the diagonals intersect each other at point O. A line segment

Mathematics
1 answer:
topjm [15]3 years ago
7 0
It will really be helpful in your solution if you draw the rectangle, its diagonal and the altitude of ΔMOP. 

By doing so, you will find that ∠MOP is equal to twice m∠AOP and that is equal to 30°. Then, m∠MOP is a vertical angle of m∠NOK which means that they are equal. Therefore, m∠NOK is also 30°. 

We know that the sum of the angles of a triangle is equal to 180°.
                m∠NOK + m∠OKN + m∠ONK = 180°
And that m∠OKN = m∠ONK
so,
                 m∠NOK + 2m∠ONK = 180°
Substituting,
                 30° + 2m∠ONK = 180°
Hence,
                        m∠ONK = 75°
You might be interested in
Assume that 140 surveys are completed. Of those surveyed, 71 responded positively to effectiveness, 60 responded positively to s
liraira [26]

Answer:

15

Step-by-step explanation:

Let n(T) denotes total surveys done i.e. n(T)=140

Let n(A) be the no. of responses to positively to effectiveness i.e. n(A)=71

Let n(B) be the no. of side effects i.e.n(B) =60

Let n(C) be the no. of responses to cost i.e. n(C)= 65

33 responded positively to both effectiveness and side effects

So, n(A∩B)=33

31 to effectiveness and cost

n(A∩C)=31

28 to side effects and cost

n(B∩C)=28

21 to none of the items

So, n(A∪B∪C)=140-21 = 119

we are supposed to find ow many responded positively to all three i.e. n(A∩B∩C)

Formula:

n(A∪B∪C)=n(A)+n(B)+n(C)-n(A∩B)-n(A∩C)-n(B∩C)+ n(A∪B∪C)

119=71+60+65-33-31-28+ n(A∪B∪C)

119=104+ n(A∪B∪C)

119-104= n(A∪B∪C)

15= n(A∪B∪C)

Hence 15 responded positively to all three

7 0
3 years ago
NEED DONE BY 8 PLEASE HELP
marusya05 [52]
Yiu need to first off start withe the first number and then get the answer
7 0
3 years ago
Area of a square is 81cm. Find the perimeter in cm.
klemol [59]

Answer:

36 cm

hope it helps have a great day

5 0
3 years ago
Read 2 more answers
What is the cube root of 27a^12?<br> A. -за^<br> B.-За<br> C.За<br> D.за^4
umka21 [38]

Answer:

Cube root of 27 a^12 will be: D 3 a^4.

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
When a whole number is multiplied by 104, how does the placement of the decimal point change?
Vera_Pavlovna [14]

Answer:

d

Step-by-step explanation:


6 0
3 years ago
Other questions:
  • Which of the binomials below is a factor or this trinomial x-2 +5x+6
    8·1 answer
  • Find the product enter answer below
    13·2 answers
  • 2 + 3(3a + a)<br> What is this simplified?
    11·1 answer
  • A person places $479 in an investment account earning an annual rate of 8.2%, compounded continuously. Using the formula V = Pe^
    13·1 answer
  • Jamie and Ryan work at the grocery store. The wages earned for the weekend are shown in the table and graph. Who gets paid more
    15·1 answer
  • PLEASE ANSWER ASAP WILL GIVE BRAINIEST ANSWER!!!!!!!!Which graph represents a direct variation between the quantities x and y?
    10·1 answer
  • What is the order pair of -x-4y=-10
    6·1 answer
  • Larry McCoy desposited three checks to his checking account he remembers that one of the checks was twice the amount of the smal
    11·1 answer
  • Can you PLEASE help me,
    11·2 answers
  • A company wants to hire the person who
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!