Angles in triangle

The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle?

Result

β =  82 °
γ =  42 °
α =  56 °

Solution:

\alpha + \beta + \gamma = 180 ^\circ \ \\ \beta /\gamma =6/8 \ \\ \alpha = 40 ^\circ + \beta \ \\ \ \\ \alpha = \dfrac{ 6 \cdot \dfrac{180-40}{ \dfrac{2\cdot6}8+1}}8 + 40 = 82 \text{ ^\circ }
\beta = \dfrac{ 6 \cdot \dfrac{180-40}{ \dfrac{2\cdot6}8+1}}8 = 42 \text{ ^\circ }
\gamma = \dfrac{180-40}{ \dfrac{2\cdot6}8+1} = 56 \text{ ^\circ }

Try another example


Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Do you have a system of equations and looking for calculator system of linear equations?
See also our trigonometric triangle calculator.

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Triangle 42
    triangle2_4 Triangle BCA. Angles A=119° B=(3y+14) C=4y. What is measure of triangle BCA=?
  2. Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  3. Reference angle
    anglemeter Find the reference angle of each angle:
  4. Factory and divisions
    factory_2 The factory consists of three auxiliary divisions total 2,406 employees. The second division has 76 employees less than 1st division and 3rd division has 212 employees more than the 2nd. How many employees has each division?
  5. Three workshops
    workers_24 There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?
  6. Three brothers
    family_13 The three brothers have a total of 42 years. Jan is five years younger than Peter and Peter is 2 years younger than Michael. How many years has each of them?
  7. Legs
    rak Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
  8. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  9. Equations - simple
    linearna_1 Solve system of linear equations: x-2y=6 3x+2y=4
  10. Linear system
    linear_eq_2 Solve a set of two equations of two unknowns: 1.5x+1.2y=0.6 0.8x-0.2y=2
  11. Linsys2
    linear_eq_3 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
  12. Two equations
    children_23 Solve equations (use adding and subtracting of linear equations): -4x+11y=5 6x-11y=-5
  13. Elimination method
    rovnice_1 Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
  14. The dormitory
    hotel_7 The dormitory accommodates 150 pupils in 42 rooms, some of which are triple and some are quadruple. Determine how many rooms are triple and how many quadruples.
  15. Mushrooms
    huby_2 Eva and Jane collected 114 mushrooms together. Eve found twice as much as Jane. How many mushrooms found each of them?
  16. Equations
    p1110617 Solve following system of equations: 6(x+7)+4(y-5)=12 2(x+y)-3(-2x+4y)=-44
  17. Three unknowns
    matrix_1 Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0