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.








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

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




Do you have a system of equations and looking for calculator system of linear equations? See also our trigonometric triangle calculator.

Next similar examples:

  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. Angles in triangle
    trigonometry 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?
  3. Family parcels
    map_4 In father will he divided the land so that the older son had three bigger part than younger son. Later elder son gave 2.5 ha field to younger and they had both the same. Determine the area of family parcel.
  4. Theatro
    divadlo_1 Theatrical performance was attended by 480 spectators. Women were in the audience 40 more than men and children 60 less than half of adult spectators. How many men, women and children attended a theater performance?
  5. Classroom
    trieda_1 There are eighty more girls in the class than boys. Boys are 40 percent and girls are 60 percent. How many are boys and how many girls?
  6. Summerjob
    bulb2_1 Three students participated in the summerjob. Altogether they earn 1780, -. Peter got a third less than John and Paul got 100,- more than Peter. How much got every one of them?
  7. Boxes
    krabice 200 boxes have been straightened in three rows. The first was 13 more than in the second, and in the second was one fifth more than in the third one. How many boxes are in each row?
  8. Pears
    hrusky Andrew, Lenka and Rasto have together 232 pears. Lenka has 28 more than Rasto and Rasto pears have 96 more than Andrew. Determine how much each of them has pears.
  9. Fifth of the number
    numbs_5 The fifth of the number is by 24 less than that number. What is the number?
  10. Book
    books_1 Alena read a book at speed 15 pages per day. If she read twice as fast she should read a book four days earlier. How many pages have a book?
  11. Dining room
    table The dining room has 11 tables (six and eight seats). In total there are 78 seats in the dining room. How many are six-and eight-seat tables?
  12. Tickets
    tickets Tickets to the zoo cost $4 for children, $5 for teenagers and $6 for adults. In the high season, 1200 people come to the zoo every day. On a certain day, the total revenue at the zoo was $5300. For every 3 teenagers, 8 children went to the zoo. How man
  13. Glass
    sklenice_1 Trader ordered from the manufacturer 200 cut glass. The manufacturer confirmed the order that the glass in boxes sent a kit containing either four or six glasses. Total sent 41 boxes. a) How many boxes will contain only 4 glasses? b) How many boxes will co
  14. Substitution
    eq1_5 solve equations by substitution: x+y= 11 y=5x-25
  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. ATC camp
    camp The owner of the campsite offers 79 places in 22 cabins. How many of them are triple and quadruple?
  17. Theorem prove
    thales_1 We want to prove the sentense: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?