Question

In a cyclic quadrilateral ABCD, if ∠A and ∠C are in the ratio 3 : 2, then we have: ∠A = ................................. and ∠B = ................................. *

2 points​

Answer 1

Given : A CYCLIC QUADRILATERAL ABCD ANGLE A AND C ARE IN THE RATIO 3:2

To Find : MEASURE OF ∠A and ∠C

Solution:

Cyclic Quadrilateral  :

Quadrilateral whose vertex lies on a circle.

Sum of opposite angles is 180°  in cyclic Quadrilateral

∠A + ∠C  = 180°

ANGLE A AND C ARE IN THE RATIO 3:2

∠A = 3k

∠C = 2K

∠A + ∠C  = 180°

=> 3k +2k = 180°

=> 5k = 180°

=> k = 36°

∠A = 3k = 3 x 36° = 108°

∠C = 2K = 2 x  36° = 72°

MEASURE OF ∠A =  108°

MEASURE OF ∠C = 72°

∠B can not be found by given information

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