Internal angles
The ABCD is an isosceles trapezoid, which holds:
|AB| = 2 |BC| = 2 |CD| = 2 |DA|:
On the BC side 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 the BC side 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°
7 years ago 5 Likes
Tips for related online calculators
You need to know the following knowledge to solve this word math problem:
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 marathon
There are 12 athletes joining the Topolcany Marathon Event. How many ways can the first, second, and third placers be chosen? - A rope
A 75m piece of rope needs to be cut in the ratio 1:4. What is the length of each piece? - Lara's sequence
Lara starts with a number less than 20. She divides it by 2 adds 6. She then divides this result by 3 her answer is 4.5 What number does she start with? - Empty rooms
In the tourist dormitory, 44 students slept in eight rooms, some of which were four-bed and others six-bed. When two beds were empty, how many four-bed and six-bed rooms were there in the dormitory?
- One muffin
Eight muffins and one drink cost $8.12. If the drink costs $1.24, find the cost of one muffin. - Mixed numbers equation
4 5/9 is the same as the sum of 2 1/3 and 5/6 times a number. What is the number? Enter your answer as a mixed number in simplest form in the box. - Negative mixed number 2
What is the product of 1 1/2 and -1 1/4? Enter your answer as a mixed number, in simplest form, in the box. - Monthly expenses
John's monthly expenses are analyzed as follows: 1/8 for stationery, 1/3 for fuel, 1/6 for parking, and the rest for food. His total expenses are 4500. Calculate the rand value of the food expenses. - Electronics price loss
Archie buys TV set for 15000. After sometime, he plans to sell it again and reduce the price by 800. What is the percent of loss?
- 13 times
1/3 times the sum of a number, and 2.6 is 4.9. What is the number? Enter your answer as a simplified mixed number in the box. - A park on map
A park has an area of ⅙ mi². On a map, the park has an area of 1 ¼ cm². On the map, how many square centimeters represent 1 mi²? - Water per day
Liam's goal is to drink 12 cups of water a day. So far, Liam has drank one-half gallon of water today. How much more water, in OUNCES, does Liam need to drink today to reach his goal of 12 cups of water per day? - Grain storage
On their farm, Adam's family maintains a storage facility that can hold 19.2 cubic yards (yd3) of grain. Since 1 yard is approximately equal to 0.9144 m, this volume can be converted to m³. - The number 10
The number of sides of two regular polygons differ by 1 the sum of the interior angles of the polygons is in the ratio of 3:2 calculate the number of sides of each polygon.
- Vidya
Vidya and Peter went for a picnic. Their mother gave them a 5-liter water bottle. Vidya consumed 2/5 of the water, and Peter consumed the remaining water. How much water did Vidya drink? How much water did Peter drink? - Percentage and fractions
Determine the correct answer by reasoning and calculating mentally. Write 46% as a fraction. ... - Nautical vs statue mile
A nautical mile is the unit of length used in sea and air navigation. A nautical mile is equal to 6,076 feet. What percent of a statue mile (5,280 ft) is a nautical mile?