MO Z7–I–6 2021
In 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.
Correct answer:
Tips for related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
See also our right triangle calculator.
See also our trigonometric triangle calculator.
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:
- geometry
- line
- similarity of triangles
- algebra
- equation
- expression of a variable from the formula
- planimetrics
- right triangle
- triangle
Units of physical quantities:
Themes, topics:
Grade of the word problem:
We encourage you to watch this tutorial video on this math problem: video1
Related math problems and questions:
- The right triangle
In the right triangle ABC with a right angle at C, we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles. - Similarity coefficient
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'. - Draw triangle
Construct an isosceles triangle ABC, if AB = 7cm, the size of the angle ABC is 47°, arms | AC | = | BC |. Measure the size of the BC side in mm. - Equilateral triangle ABC
In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near point C, and point M lies on one-third of the side of the AC side closer to point A. Find what part of the ABC triangle contains the triangl - Rhomboid
The rhomboid sides' dimensions are a= 5cm, b = 6 cm, and the angle's size at vertex A is 60°. What is the length of the side AC? - Identical 8831
In the triangle ABC, the point P lies closer to point A in the third of the line AB, the point R is closer to the point P in the third of the line P, and the point Q lies on the line BC so that the angles P CB and RQB are identical. Determine the ratio of - Angles
In the triangle ABC, the ratio of angles is α:β = 4:5. The angle γ is 36°. How big are the angles α and β? - MO - triangles
On the AB and AC sides of the ABC triangle lies successive points E and F, and on segment EF lie point D. The EF and BC lines are parallel. It is true this ratio FD:DE = AE:EB = 2:1. The area of the ABC triangle is 27 hectares, and line segments EF, AD, a - Intersection 5413
In the acute triangle KLM, the angle KLM is 68°. Point V is the intersection of the altitudes, and P is the foot of the altitude on the side LM. The angle P V M axis is parallel to the side KM. Compare the sizes of angles MKL and LMK. - Construction
Construct the triangle ABC if you know: the size of the side AC is 6 cm, the size of the angle ACB is 60°, and the distance of the center of gravity T from the vertex A is 4 cm. (Sketch, analysis, notation of construction, construction) - Isosceles 2588
Given an isosceles trapezoid ABCD, in which | AB | = 2 | BC | = 2 | CD | = 2 | DA | holds. On its side BC, the point K is such that | BK | = 2 | KC |; on its CD side, the point L is such that | CL | = 2 | LD |, and on its DA side, the point M is such that - Angles of elevation
From points A and B on level ground, the angles of elevation of the top of a building are 25° and 37°, respectively. If |AB| = 57m, calculate, to the nearest meter, the distances of the top of the building from A and B if they are both on the same side of - Triangles
Find out whether the 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' - Triangle ABC
In a triangle ABC with the side BC of length 2 cm. Point K is the middle point of AB. Points L and M split the AC side into three equal lines. KLM is an isosceles triangle with a right angle at point K. Determine the lengths of the sides AB, AC triangle A - Triangle's centroid
In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid), and the point S is the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side t - Calculate 3208
Calculate the size of the sides and angles of the triangle ABC if you know vc = 28, α = 51 ° 19 ', β = 67 ° 38'. - Quadrilateral 42151
Calculations from geometry: The ratios of the sides of the quadrilateral are 3 : 6:4.5 : 3.5. Calculate their lengths if the circumference is 51 cm. The sizes of the angles in the quadrilateral are equal to 29°30', 133°10', and 165°20'. What is the size o
