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?

Correct answer:

KLM =  55 °
KML =  55 °

Step-by-step explanation:

$$\begin{gathered} \mathrm{\angle }MKL=70^{\circ } \\ \mathrm{\angle }MKL+KLM+KML=180^{\circ } \\ \delta =90^{\circ }-KLM \\ \mathrm{\angle }KMX=90-\mathrm{\angle }MKL=90-70=20^{\circ } \\ 2\delta =90^{\circ }-\mathrm{\angle }KMX \\ \delta =(90-\mathrm{\angle }KMX)\mathrm{/}2=(90-20)\mathrm{/}2=35^{\circ } \\ \mathrm{\angle }KLM=90-\delta =90-35=55^{\circ } \end{gathered}$$

$\mathrm{\angle }KML=180-\mathrm{\angle }MKL-\mathrm{\angle }KLM=180-70-55=55^{\circ }$

Try another example

Related math problems and questions:

• Inner angles
  The magnitude of the internal angle at the main vertex C of the isosceles triangle ABC is 72°. The line p, parallel to the base of this triangle, divides the triangle into a trapezoid and a smaller triangle. How big are the inner angles of the trapezoid?
• MO Z7–I–6 2021
  In the triangle ABC, point D lies on the AC side and point E on the BC side. The sizes of the angles ABD, BAE, CAE and CBD are 30°, 60°, 20° and 30°, respectively. Find the size of the AED angle.
• 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|. Dete
• Outer angles
  The outer angle of the triangle ABC at the A vertex is 71°40 ' outer angle at the vertex B is 136°50'. What size has the inner triangle angle at the vertex C?
• Triangles
  Find out whether given sizes of the angles can be interior angles of a triangle: a) 23°10',84°30',72°20' b) 90°,41°33',48°37' c) 14°51',90°,75°49' d) 58°58',59°59',60°3'
• Similarity
  Are two right triangles similar to each other if the first one has an acute angle 70°, and the second one has an acute angle 20°?
• KLM triangle
  Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees.
• Right angle
  In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
• 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.
• In a 2
  In a thirteen sided polygon, the sum of five angles is 1274°, four of the eight angles remaining are equal and the other four are 18° less than each of the equal angles. Find the angles. .
• 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?
• Powerplant chimney
  From the building window at the height of 7.5 m, we can see the top of the factory chimney at an altitude angle of 76° 30 ′. We can see the chimney base from the same place at a depth angle of 5° 50 ′. How tall is the chimney?
• A kite
  ABCD is a kite. Angle OBC = 20° and angle OCD = 35°. O is the intersection of diagonals. Find angle ABC, angle ADC and angle BAD.
• The ladder
  The ladder touch on a wall at a height of 7.5 m. The angle of the inclination of the ladder is 76°. How far is the lower end of the ladder from the wall?
• n-gon
  Gabo draws n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon?
• Inner angles
  The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
• Angles of a triangle
  In triangle ABC, the angle beta is 15° greater than the angle alpha. The remaining angle is 30° greater than the sum of the angles alpha and beta. Calculate the angles of a triangle.