In a Trapezium ABCD ab is parallel to dc angle A is equal to angle D 4ratio 5 and b is equal to angle C 3 ratio 2
find the angles of the trapezium
Answers
Answer:
Step-by-step explanation:
a=4/5d
b=3/2c
a+d and c+b each =180 angle on same side of transeversal
4/5d+d=180
9/5d=180
d=5/9*180
d=100,a=80 supplementry
3/2c+c=180
c=2/5*180
c=72
so b=108
Answer:
The angles A, B, C, and D are 80°, 108°, 72°, and 100°.
Step-by-step explanation:
Given:
AB || CD
A:D = 4:5 ⇒ A = (4/5)D
B:C = 3:2 ⇒ B = (3/2)C
To find:
∠A, ∠B, ∠C, and ∠D
Solution:
It is given that side AB is parallel to side CD. So, the side AD will act as a transversal.
Therefore, angle A and angle D will form a pair of interior angles whose sum will be equal to 180°.
∠A + ∠D = 180°
(4/5)D + D = 180°
(9/5)D = 180
D = (180×5)/9
D = 20×5
D = 100°
A = (4/5)D
A = (4/5) 100
A = 4×20
A = 80°
Similarly, side BC will act as a transversal to AB and CD.
Therefore, angle B and angle C will form a pair of interior angles whose sum will be equal to 180°.
∠B + ∠C = 180°
(3/2)C + C = 180°
(5/2)C = 180
C = (180×2)/5
C = 36×2
C = 72°
B = (3/2)C
B = (3/2) 72
B = 3×36
B = 108°
Therefore, the angles of the trapezium ABCD are 80°, 108°, 72°, and 100° respectively.
#SPJ3