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.

Result

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

Solution:

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

Calculated by our linear equations calculator.

Try another example

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

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.

2 years ago  Like

Next similar math problems:

1. Internal angles IST
   Determine internal angles of isosceles trapezium ABCD /a, c are the bases/ and if: alpha:gamma = 1:3
2. Angle
   Determine the size of the smallest internal angle of a right triangle which angles forming the successive members of the arithmetic sequence.
3. Alfa beta gama
   The triangle's an interior angle beta is 10 degrees greater than the angle alpha and gamma angle is three times larger than the beta. Determine the size of the interior angles.
4. In a 2
   In a thirteen sided polygon, the sum of five angles is 1274°, four of the eight angles remaining are equal and the other four are 18° less than each of the equal angles. Find the angles. .
5. Angles in ratio
   The size of the angles of the triangle are in ratio x: y = 7: 5 and the angle z is 42° lower than the angle y. Find size of the angles x, y, z.
6. Angles of the triangle
   ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC.
7. Isosceles trapezoid
   Perimeter of the isosceles trapezoid is 48 cm. One side is two times greater than the second side. Determine the dimensions of the trapezoid.
8. Largest angle of the triangle
   What is the largest angle of the triangle if the second angle is 10° greater than twice the first and the third is 30° smaller than the second?
9. Linsys2
   Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
10. Ball game
    Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.
11. Stones 3
    Simiyu and Nasike each collected a number of stones in an arithmetic lesson. If Simiyu gave Nasike 5 stones, Nasike would have twice as many stones as Simiyu. If initially, Simiyu had five stones less than Nasike how many stones did each have?
12. Warehouses
    In the three warehouses, a total of 70 tons of grain was stored. In the second warehouse was stored 8.5t less and in the third 3.5t more than in the first. How many tons of grain was stored in each warehouse?
13. Null points
    Calculate the roots of the equation: ?
14. Children
    The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group?
15. Men, women and children
    On the trip went men, women and children in the ratio 2:3:5 by bus. Children pay 60 crowns and adults 150. How many women were on the bus when a bus was paid 4,200 crowns?
16. Geometric sequence 5
    About members of geometric sequence we know: ? ? Calculate a₁ (first member) and q (common ratio or q-coefficient)
17. Theorem prove
    We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?