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.

Correct answer:

A =  80 °
B =  60 °
C =  120 °
D =  100 °

Step-by-step explanation:

A = 4/5 D
B = 3x-15
C = 4x+20
A+D = 180
B+C = 180

A = 4/5•D
B = 3•x-15
C = 4•x+20
A+D = 180
B+C = 180

5A-4D = 0
B-3x = -15
C-4x = 20
A+D = 180
B+C = 180

A = 80
B = 60
C = 120
D = 100
x = 25

Our linear equations calculator calculates it.

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Showing 1 comment:
Let Angle A=4x, B= 3x-15, C=4x+20 and D=5x.

Using the property that sum of adjacent angles = 180 we get:

A + D = 180 or 4x+5x=180.
Solving we get x=20.
Substituting we get: A=80, B=100

Similarly, B+C=180 or
Solving we get x=25
Substituting we get: B=60, D=120.


Tips to 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 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:

  • Internal angles
    mo-klm 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
  • Sum of inner angles
    angle-sum-of-polygon Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees.
  • Dried fruit
    hrozienka The manufacturer produces a mixture of dried fruit. He purchased: 10kg pineapple for 200 Kc/kg 2kg papaya for 180 kc/kg 1kg of banana for 400 Kc/kg How many kgs of raisin for 80 Kc/kg must be put into the mix by the manufacturer so that the production pri
  • Dirty road
    car Mr. Smith is on a road trip to a remote disc golf course 180km away. He travels part of the way at 100km/h along the highway, and part of the way at 50km/h along dirt roads. If it took 2 hours to get there, how many hours did he spend on dirt roads?
  • Internal angles IST
    licho Determine internal angles of isosceles trapezium ABCD /a, c are the bases/ and if: alpha:gamma = 1:3
  • Euler problem
    euler Someone buys a 180 tolars towels. If it was for the same money of 3 more towels, it would be 3 tolars cheaper each. How many were towels?
  • The rescue helicopter
    helicopter The rescue helicopter is above the landing site at a height of 180m. The site of the rescue operation can be seen from here at a depth angle of 52° 40 '. How far will the helicopter land from the rescue site?
  • Rotary bodies
    conecylinder The rotating cone and the rotary cylinder have the same volume of 180 cm3 and the same height v = 15 cm. Which of these two bodies has a larger surface area?
  • Internal angles
    angle One internal angle of the triangle JAR is 25 degrees. The difference is the size of the two others is 15°. Identify the size of these angles.
  • Total displacement
    stroke_bore_engine Calculate total displacement of the 4-cylinder engine with the diameter of the piston bore B = 6.6 cm and stroke S=2.4 cm of the piston. Help: the crankshaft makes one revolution while the piston moves from the top of the cylinder to the bottom and back t
  • Lighthouse
    maiak The man, 180 cm tall, walks along the seafront directly to the lighthouse. The male shadow caused by the beacon light is initially 5.4 meters long. When the man approaches the lighthouse by 90 meters, its shadow shorter by 3 meters. How tall is the lighth
  • Internal angles
    triangle Find the internal angles of the triangle ABC if the angle at the vertex C is twice the angle at the B and the angle at the vertex B is 4 degrees smaller than the angle at vertex A.
  • Fence
    fence How many meters of fencing it is required to purchase if our garden is rectangular measuring 20 m and 180 dm.
  • Trapezium
    lichobeznik_mo_z8 The lengths of parallel sides of a trapezium are (2x+3) and (x+8), and the distance between them is (x+4). if the area of the trapezium is 590, find the value of x.
  • Worker's performance
    plot 15 workers paint 180 m fence in 3 days. In how many days will 9 workers paint a 360 m fence? We assume that each worker have the same, constant and unchangeable performance.
  • Central park in city
    park The city park has the shape of a rectangle of 180 meters in length and 120 meters in width. People make their walk through the center of the park from one corner to the second. Calculate how many meters this way is shorter than they walked along the path
  • Inner angles
    rr_triangle3 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?