Question

In a cyclic quadrilateral A B C D . Measurement of angle A =thrice of angle C. Find the measurement of the angle A.

Answer 1

In a cyclic quadrilateral, opposite angles are supplementery, i.e. their sum is 180°

Angle A and Angle C lies opposite to each other

=> angle A + angle C = 180°

Given that angle A = 3 times angle C

=> angle A = 3 × C

Now angle A + angle C = 180°

=> 3C + C = 180°

=> 4C = 180°

=> C = 180/4

=> C = 45°

Measure of angle C is 45°


Angle A + angle C = 180°

=> angle A = 180 - C

=> angle A = 180 - 45

=> angle A = 135°

Hope it helps dear friend ☺️✌️