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
VashaNatasha [74]
3 years ago
8

Find the value of each variable. PLEASE HELP ME

Mathematics
1 answer:
Nuetrik [128]3 years ago
6 0

Given:

A quadrilateral DEFG inscribed in a circle.

m\angle D=60^\circ, m\angle E=m^\circ, m\angle F=2k^\circ, m\angle G=60^\circ

To find:

The value of variables m and k.

Solution:

If a quadrilateral is inscribed in a circle then it is a cyclic quadrilateral. The opposite angles of a cyclic quadrilateral angle supplementary angles.

Quadrilateral DEFG inscribed in a circle. So, quadrilateral DEFG is a cyclic quadrilateral.

m\angle D+m\angle F=180^\circ                [Supplementary angle]

60^\circ+2k^\circ=180^\circ

2k^\circ=180^\circ-60^\circ

2k^\circ=120^\circ

Divide both sides by 2.

k^\circ=\dfrac{120^\circ}{2}

k^\circ=60^\circ

k=60

Similarly,

m\angle E+m\angle G=180^\circ

m^\circ+60^\circ=180^\circ

m^\circ=180^\circ-60^\circ

m^\circ=120^\circ

m=120

Therefore, the values of the variables are m=120 and k=60.

You might be interested in
Find the value of the missing coefficient in the factored form of 8f^3-216g^3
adoni [48]

Answer:

The value of the missing coefficient is 12

Step-by-step explanation:

* Lets explain how to factorize the difference of two cubes

- The factorization of the difference of two cubes like a³ - b³, is a

  product of a binomial and trinomial

- The binomial is the cube root of the first term and the second term

∵ The ∛a³ = a and ∛b³ = b

∴ The binomial is (a - b)

- We will find the trinomial from the binomial by square the 1st term

 of the binomial and multiply the 1st term and the 2nd term of the

 binomial with opposite sign of the binomial and square the 2nd

 term of the binomial

∴ The trinomial is (a² + ab + b²

∴ The factorization of (a³ - b³) is (a - b)(a² + ab + b²)

* Lets solve the problem

∵ 8f³ - 216g³ is the difference of two cubes

∵ ∛(8f³) = 2f

∵ ∛(216g³) = 6g

∴ The binomial is (2f - 6g)

- Lets make the trinomial

∵ (2f)² = 4f²

∵ (2f)(6g) = 12fg

∵ (6g)² = 36g²

∴ The trinomial = (4f² + 12fg + 36g²)

∴ The factorization of 8f³ - 216g³ = (2f - 6g)(4f² + 12fg + 36g²)

∴ The value of the missing coefficient is 12

7 0
3 years ago
I rlly need help with this
lakkis [162]

You need to give more info so like show more of the question

5 0
2 years ago
Read 2 more answers
Write at least 5 arithmetic sequence and determine the common difference
Margarita [4]

Answer: 1,6,11,16,21,26

Step-by-step explanation:

The common difference is 5 (n+5)

7 0
2 years ago
Read 2 more answers
Find the coordinates of the point (x, y)<br> shown on the unit circle.<br> X=
wel

Answer:

purrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
YOU BE THE TEACHER Your friend finds the sum.
il63 [147K]

Answer: My friend is correct.

Step-by-step explanation:

<em>Adding a negative is the same as subtracting a positive.</em>

9 + (-6) = 3

9 - 6 = 3

3 = 3

Hope this helps! Have a great day!

5 0
2 years ago
Read 2 more answers
Other questions:
  • Given a segment with endpoints A and B, what figure can you contrust using the steps below?
    13·2 answers
  • What is the equation of the line in slope-intercept form? Line on a coordinate plane. The line runs through points begin ordered
    12·1 answer
  • please help!! Assume the given triangular prism and rectangular prism have equal cross sections. Also assume the length and widt
    10·2 answers
  • A nickel, a dime, and a quarter are touching as shown. Tangents are drawn from point A to both sides of each coin. In a short pa
    9·1 answer
  • I need help what is -0.5 _ -0.2​
    15·1 answer
  • You have already saved $55. You can earn $9 per hour at your job. You are saving for a bicycle that costs $199. What inequality
    6·2 answers
  • Find the axis of symmetry and the vertex of the graph f(x)=2x-4x
    12·1 answer
  • Help me pleaseeeeeee
    6·2 answers
  • What is the area in square units of the figure shown below??help asap!don't share links or anything pleasee
    9·1 answer
  • Are these equivalent ratios?<br> 24:32<br> and<br> 18:24
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!