Internal angles

The ABCD is an isosceles trapezoid, which holds:
|AB| = 2 |BC| = 2 |CD| = 2 |DA|:

On its side BC is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA the point M is such that | DM | = 2 |MA|. Determine the internal angles of the KLM triangle.

Result

∠KLM =  120 °
∠LMK =  30 °
∠MKL =  30 °







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

Showing 1 comment:
#1
Math student
Help. First, look at the inner angles of the ABCD trapezoid.

Solution. It follows from the assumptions that the center line of the AB segment with the vertices C and D divides the ABCD trapezoid into three identical equilateral triangles. Therefore, the magnitude of internal angles in the trapezoid at A and B vertices is equal to 60 °
And at the C and D vertices 120 °. It follows from the specification that the triangles LCK and MDL are the same (according to the sentence above). Therefore, both the KL and LM lines and the designated pairs of angles are the same; The magnitudes of these angles are denoted α and β. The triangle KLM is isosceles and the angles at the base are the same; Their size is denoted by δ and the size of the angle KLM is denoted by γ.

From the sum of the inner angles in the KCL triangle we derive
α + β = 180° − 120° = 60°

The sum of the three marked angles with the vertex L is a straight angle, therefore
γ = 180° − (α + β) = 120°
Finally, we deduce the sum of inner angles in the triangle KLM
δ = (180° − 120°)/2 = 30°

The internal angles of the triangle KLM are 30° and 120°

avatar









To solve this example are needed these knowledge from mathematics:

See also our trigonometric triangle calculator. Try conversion angle units angle degrees, minutes, seconds, radians, grads.

Next similar examples:

  1. Rhombus ABCD
    rhombus6 Rhombus ABCD, |AC| = 97 cm, |BD| = 35 cm. Calculate the perimeter of the rhombus ABCD.
  2. Is right?
    rtriangle Is triangle with sides 51, 56 and 77 right triangle?
  3. Triangle SAS
    triangle_iron Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°.
  4. Road
    12perctent The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
  5. River
    river From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river.
  6. Triangular prism
    prism3s_1 Calculate the volume of a triangular prism 10 cm high, the base of which is an equilateral triangle with dimensions a = 5 cm and height va = 4,3 cm
  7. Regular 5-gon
    5gon_2 Calculate area of the regular pentagon with side 7 cm.
  8. Square and circles
    kruznica_stvorec_1 Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
  9. Garden
    garden_1 Area of square garden is 4/5 of triangle garden with sides 24 m, 15 m and 15 m. How many meters of fencing need to fence a square garden?
  10. Short cut
    direct_route Imagine that you are going to the friend. That path has a length 270 meters. Then turn left and go another 1810 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
  11. Rectangle
    rectangle_inscribed_circle The rectangle is 31 cm long and 28 cm wide. Determine the radius of the circle circumscribing rectangle.
  12. Right triangle Alef
    r_triangle The area of a right triangle is 294 cm2, the hypotenuse is 35 cm long. Determine the lengths of the legs.
  13. Axial section
    cone2 Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
  14. Gimli Glider
    gimli_glider Aircraft Boeing 767 lose both engines at 45000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1870 feet and maintain constant speed 212 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate
  15. Triangular prism
    prism_4 Calculate the surface of a regular triangular prism with a bottom edge 8 of a length of 5 meters and an appropriate height of 60 meters and prism height is 1 whole 4 meters.
  16. Right Δ
    ruler Right triangle has length of one leg 51 cm and length of the hypotenuse 85 cm. Calculate the height of the triangle.
  17. Circle chord
    circleChord What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?