The measures of the angles of the quadrilateral ABCD are in the ratio 4 2:3:4:1, Determine the type of quadrilateral?
Answers
Answer:
Trapezium
Step-by-step explanation:
Let the angles of the quadrilateral in degrees be =2a,3a,4a and a
Since the sum of angles of a quadrilateral =360
o
,
2a+3a+4a+a=360
o
10a=360
o
a=36
So,
the angles of the quadrilateral are =2a=72
o
,3a=108
o
,4a=144
o
and
a=36
Suppose
∠A=72
o
and ∠B=108
o
Sum of ∠A and ∠B=72
o
+108
o
=180
o
This means, AB is a transversal to the parallel sides AD and BC as the sum of
interior angles on the same side of transversal is 180
o
Hence, AD∥BC and ABCD is a trapezium.
Step-by-step explanation:
Trapezium
Let the angles of the quadrilateral in degrees be =2a,3a,4a and a
Since the sum of angles of a quadrilateral =360
o
,
2a+3a+4a+a=360
o
10a=360
o
a=36
So,
the angles of the quadrilateral are =2a=72
o
,3a=108
o
,4a=144
o
and
a=36
Suppose
∠A=72
o
and ∠B=108
o
Sum of ∠A and ∠B=72
o
+108
o
=180
o
This means, AB is a transversal to the parallel sides AD and BC as the sum of
interior angles on the same side of transversal is 180
o
Hence, AD∥BC and ABCD is a trapezium.