# 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:

**Showing 1 comment:**

**Partho**

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

3x-15+4x+20=180

Solving we get x=25

Substituting we get: B=60, D=120.

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

3x-15+4x+20=180

Solving we get x=25

Substituting we get: B=60, D=120.

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 trigonometric triangle calculator.

See also our trigonometric triangle calculator.

#### You need to know the following knowledge to solve this word math problem:

#### Units of physical quantities:

#### Grade of the word problem:

We encourage you to watch this tutorial video on this math problem: video1

## Related math problems and questions:

- Trapezium ABCD

The figure shows 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 - Four-digit 55481

Find all four-digit abcd numbers to which: abcd = 20. ab + 16. cd, where ab and cd are double digits numbers from digits a, b, c, and d. - Swimming pool

A swimming pool 30 meters long is filled with water to a depth of 1 meter at the shallow end, and 5 meters at the deep end, and abcd the vertical area of the pool has the shape of a trapezium with the area given by S(abcd)= 1/2 (ab + cd) x ad. What is the - Parallel and orthogonal

I need math help in this problem: a=(-5, 5 3) b=(-2,-4,-5) (they are vectors) Decompose the vector b into b=v+w where v is parallel to a and w is orthogonal to a, find v and w - Trapezium

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. - Trapezoid RT

The plot has a shape of a rectangular trapezium ABCD, where ABIICD with a right angle at the vertex B. side AB has a length of 36 m. The lengths of the sides AB and BC are in the ratio 12:7. Lengths of the sides AB and CD are a ratio of 3:2. Calculate con - One trapezium

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

The ABCD trapezoid has parallel sides AB and CD. The E point lies on the AB side. The segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment. - Consecutive Interior Angles

PQRS is a trapezium in which PQ is parallel to SR and ∠P = 130 ̊, ∠Q = 110 ̊. Find the remaining angles. - Find the 10

Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular and parallel. What angle does each line make with the x-axis, and find the angle between the lines? - Suppose 10

Suppose 4+7i is a solution of 5z2+Az+B=0, where A, B∈R. Find A and B. - Four-digit number

For a four-digit number abcd, ab: bc = 1:3 and bc: cd = 2:1 (ab, bc and cd are two-digit numbers from digits a, b, c, d). Find this number(s). - Trapezoid ABCD

ABDC is a trapezoid in which AB and CD are parallel sides measuring 6 and 9, respectively. Angles ABC and BCD are both right angles. Find the length of segment BD. - Vector - basic operations

There are given points A [-9; -2] B [2; 16] C [16; -2] and D [12; 18] a. Determine the coordinates of the vectors u=AB v=CD s=DB b. Calculate the sum of the vectors u + v c. Calculate the difference of vectors u-v d. Determine the coordinates of the vecto - trapezium 3428

Given is a trapezoid ABCD with bases AB, CD. Let K be side AB's midpoint, and point L be side CD's midpoint. The area of triangle ALB is 15 cm^{2}, and the area of triangle DKC is 10 cm². Calculate the area of trapezium ABCD. - Trapezoid 70454

Construct a trapezoid ABCD (AB // CD): | AB | = 7cm | BC | = 3.5cm | CD | = 4cm The magnitude of the angle ABC = 60° - Isosceles triangle 9

There is an isosceles triangle ABC where AB= AC. The perimeter is 64cm, and the altitude is 24cm. Find the area of the isosceles triangle.