# 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.

|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.

### Correct answer:

**Showing 1 comment:**

**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°

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°

Tips to related online calculators

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

## Related math problems and questions:

- 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 the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont - 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. - 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? - Pentagon

The signboard has the shape of a pentagon ABCDE, in which the line BC is perpendicular to the line AB and EA is perpendicular to the line AB. Point P is the heel of the vertical starting from point D on line line AB. | AP | = | PB |, | BC | = | EA | = 6dm - Trapezium internal angles

A trapezium where AB is parallel to CD, has angle A : angle D = 4 :5, angle B = 3x-15 and angle C = 4x+20. Find angle A, B, C and D. - MO Z8–I–6 2018

In the KLMN trapeze, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line. - 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? - Trapezium ABCD

In the figure, ABDC is a trapezium in which AB || CD. line segments RN and LM are drawn parallel to AB such that AJ=JK=KP. If AB=0.5m and AP=BQ=1.8m, find the lengths of AC, BD, RN and LM. angle D=angle C=60 - Diagonals at right angle

In the trapezoid ABCD, this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD? - Diagonal intersect

isosceles trapezoid ABCD with length bases | AB | = 6 cm, CD | = 4 cm is divided into 4 triangles by the diagonals intersecting at point S. How much of the area of the trapezoid are ABS and CDS triangles? - Triangle in a square

In a square ABCD with side a = 6 cm, point E is the center of side AB, and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides. - Isosceles - isosceles

It is given a triangle ABC with sides /AB/ = 3 cm /BC/ = 10 cm, and the angle ABC = 120°. Draw all points X such that true that BCX triangle is an isosceles and triangle ABX is isosceles with the base AB. - Trapezoid thirds

The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side. The segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment. - One trapezium

One trapezium has AB=24M, BC=36M, CD=80M, DA=80M long sides. Find the area. - In triangle

In triangle ABC, the magnitude of the internal angle gamma is equal to one-third of the angle alpha. The size of the angle beta is 80 degrees larger than the size of the gamma angle. Calculate the magnitudes of the interior angles of the triangle ABC. - MO - triangles

On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB seg - Rhombus construction

Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it touching all sides...