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)

Correct answer:

∠ DMO =  60 °

Step-by-step explanation:

$$\begin{gathered} \mathrm{\angle }MOH=180\mathrm{°}-\alpha -4\alpha =180\mathrm{°}-5\alpha \\ 90\mathrm{°}+(\alpha +\alpha )+(180\mathrm{°}-5\alpha )=180\mathrm{°} \\ 90\mathrm{°}=3\alpha \\ \alpha =30\mathrm{°} \\ \mathrm{\angle }DMO=2\alpha =2\cdot 30\mathrm{°}=60\text{°} \end{gathered}$$

Try another example

Related math problems and questions:

• Supplementary angles
  One of the supplementary angles are three times larger than the other. What size is larger of supplementary angles?
• Flowerbed
  The flowerbed has the shape of an obtuse isosceles triangle. Arm has a size 5.5 meters, and an angle opposite to the base size is 94°. What is the distance from the base to the opposite vertex?
• The second
  The second angle of a triangle is the same size as the first angle. The third angle is 12 degrees larger than the first angle. How large are the angles?
• Acute triangle
  In the acute triangle KLM, V is the intersection of its heights and X is the heel of height to the side KL. The axis of the angle XVL is parallel to the side LM and the angle MKL is 70°. What size are the KLM and KML angles?
• Ratio of triangles areas
  In an equilateral triangle ABC, the point T is its centre of gravity, the point R is the image of the point T in axial symmetry, along the line AB, and the point N is the image of the point T in axial symmetry along the line BC. Find the ratio of the area
• Alfa, beta, gama
  In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC.
• Chord MN
  Chord MN of circle has distance from the center circle S 120 cm. Angle MSN is 64°. Determine the radius of the circle.
• Angle
  A straight line p given by the equation y = (-8)/(6) x +78. Calculate the size of angle in degrees between line p and y-axis.
• Angles ratio
  In a triangle ABC true relationship c is less than b and b is less than a. Internal angles of the triangle are in the ratio 5:4:9. The size of the internal angle beta is:
• Railway
  Between points A, B, whose horizontal distance is 1.5 km railway line has 8promile climb. Between points B, C with horizontal distance of 900 m is climb 14promile. Calculate differences of altitudes between points A and C.
• 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?
• Smallest internal angle
  Calculate what size has the smallest internal angle of the triangle if values of angles α:β:γ = 3:4:8
• Perpendicular
  What is the slope of the perpendicular bisector of line segment AB if A[9,9] and B[9,-2]?
• Angle of two lines
  There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV.
• Tree
  Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree?
• Lines
  How many lines can be draw with 8 points, if three points lie on one line and the other any three points do not lie on the same line?
• Three parallels
  The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.