Question

IN A CYCLIC QUADRILATERAL ABCD ANGLE A AND C ARE IN THE RATIO 3:2 THEN MEASURE OF

Answer 1

Answer:

The angles are 108° and 72°.

Step-by-step explanation:

Ratio --> 3:2

Let angles be 3x and 2x.

We know that the sum of opposite angles in a cyclic quadrilateral is 180°.

Thus, 3x + 2x = 180°

=> 5x = 180°

∴ x = 180/5 => 36°

Therefore, the angles are 3x = 3(36)° => 108° and 2x = 2(36)° => 72°.

Answer 2

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°

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