Question

One angle of a cyclic trapezium is triple the other. find the measure of the smaller angle

Answer 1

If all the vertices of a trapezium lie on a circle, then it is a cyclic trapezium.

Opposite angles of a cyclic trapezium are supplementary.
Adjacent angles of a cyclic trapezium are supplementary.
A cyclic trapezium is an isosceles trapezium in which non-parallel sides are equal.
let x be the small angle
since opposite angles are supplementary,
then x+3x=180
4x=180
x=45 degrees.