Obtuse angle

The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image)

Result

∠ DMO =  60 °

Solution:

∠MOH=180∘−α−4α=180∘−5α 90∘+(α+α)+(180∘−5α)=180∘ 90∘=3α α=30∘  ∠DMO=2α=2⋅30∘=60∘\angle MOH = 180^\circ -\alpha - 4 \alpha = 180^\circ -5\alpha \ \\ 90^\circ +(\alpha +\alpha )+(180^\circ -5\alpha ) = 180^\circ \ \\ 90^\circ = 3 \alpha \ \\ \alpha = 30^\circ \ \\ \ \\ \angle DMO= 2 \alpha = 2 \cdot 30^\circ = 60 ^\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
See also our right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  1. Slope
    slope_1 Find the slope of the line: x=t and y=1+t.
  2. The cable car
    lanovka The cable car has a length of 3,5 kilometers and an angle of climb of 30 degrees. What is the altitude difference between Upper and Lower Station?
  3. Climb
    aircraft_ascend For horizontal distance 4.2 km road rise by 6.3 m. Calculate the road pitch in ‰ (permille, parts per thousand).
  4. Right angle
    triangles_1 If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6
  5. Find the 9
    obtuse_triangle_1 Find the missing angle in the triangle and then name triangle. Angles are: 95, 2x+15, x+3
  6. Right triangles
    PT How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget to the triangle inequality).
  7. Similarity coefficient
    trig12 The triangles ABC and A "B" C "are similar to the similarity coefficient 2. The sizes of the angles of the triangle ABC are α = 35° and β = 48°. Find the magnitudes of all angles of triangle A "B" C ".
  8. Double ladder
    rr_rebrik The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
  9. Height 2
    1unilateral_triangle Calculate the height of the equilateral triangle with side 38.
  10. Three days
    skolske-zosity_1 During the three days sold in stationery 1490 workbooks. The first day sold about workbooks more than third day. The second day 190 workbooks sold less than third day. How many workbooks sold during each day?
  11. Mom and daughter
    family_1 Mother is 39 years old. Her daughter is 15 years. For many years will mother be four times older than the daughter?
  12. Three friends
    oriental The three friends spent 600 KC in a teahouse. Thomas paid twice as much as Paul. Paul a half less than Zdeněk. How many each paid?
  13. Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  14. Is right triangle
    triangle_1111_4 Decide if the triangle XYZ is rectangular: x = 4 m, y = 6 m, z = 4 m
  15. Double ladder
    dvojak The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
  16. Tunnels
    Mysky Mice had built an underground house consisting of chambers and tunnels: • each tunnel leading from the chamber to the chamber (none is blind) • from each chamber lead just three tunnels into three distinct chambers, • from each chamber mice can get to an
  17. Test points
    test_2 If you earned 80% of the possible 40 points, how many points did you miss to get 100%?