Angles in ratio

The size of the angles of the triangle are in ratio x: y = 7: 5 and the angle z is 42° lower than the angle y. Find size of the angles x, y, z.

Result

x =  91.412 °
y =  65.294 °
z =  23.294 °

Solution:


5x = 7y
z = y-42
x+y+z=180

5x-7y = 0
y-z = 42
x+y+z = 180

x = 155417 ≈ 91.411765
y = 111017 ≈ 65.294118
z = 39617 ≈ 23.294118

Calculated by our linear equations calculator.

Try another example






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




To solve this verbal math problem are needed these knowledge from mathematics:

Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation? See also our trigonometric triangle calculator.

Next similar math problems:

  1. Angles of the triangle
    angles ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC.
  2. Reference angle
    anglemeter Find the reference angle of each angle:
  3. Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  4. The larger
    59_number The larger of two numbers is nine more than four times the smaller number. The sum of the two numbers is fifty-nine. Find the two numbers.
  5. 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?
  6. Blackberries
    cernice Daniel, Jolana and Stano collected together 34 blackberries. Daniel collected 8 blackberries more than Jolana, Jolana 4 more than Stano. Determine the number blackberries each collected .
  7. Children
    children_3 The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group?
  8. Three figures - numbers
    numbers34 The sum of three numbers, if each is 10% larger than the previous one, is 662. Determine the figures.
  9. Equations
    p1110617 Solve following system of equations: 6(x+7)+4(y-5)=12 2(x+y)-3(-2x+4y)=-44
  10. Elimination method
    rovnice_1 Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
  11. Two numbers
    maxwells-equation We have two numbers. Their sum is 140. One-fifth of the first number is equal to half the second number. Determine those unknown numbers.
  12. Equations - simple
    linearna_1 Solve system of linear equations: x-2y=6 3x+2y=4
  13. Two equations
    children_23 Solve equations (use adding and subtracting of linear equations): -4x+11y=5 6x-11y=-5
  14. Linsys2
    linear_eq_3 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
  15. Football match 4
    futball_ball In a football match with the Italy lost 3 goals with Germans. Totally fell 5 goals in the match. Determine the number of goals of Italy and Germany.
  16. 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.
  17. 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?