For cyclic quadrilateral ABCD ,angle A-angle C=20, then find angle A?

Question

Answer

+ A+C = 180. [ Sum of opposite angles of a cyc. quadrilateral ]
+ A-C = 20. [ GIVEN ]
---------------------
2A = 200
---------------------
A = 200/2
A = 100

SO,
| angle A = 100* |

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Answer

Opposite angles sum 180 degrees in Cyclic Quadrilateral
so ang A + ang C =180
ang A - ang C = 20
add above 2 equations
2 ang A = 200
ang A = 100
answer : ang A = 100

Answer

Given: Cyclic quadrilateral ABCD, angle A - angle C = 20

To Find: Angle A

Solution:

Introduction:
A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. In a cyclic quadrilateral, opposite angles are supplementary, meaning the sum of the opposite angles is 180 degrees.

Approach:
To find angle A in cyclic quadrilateral ABCD, we can use the property that opposite angles are supplementary. Since angle A and angle C are opposite angles, their sum is 180 degrees.

Step-by-Step Solution:

1. Let's assume that angle A is x degrees.
2. According to the given condition, angle A - angle C = 20.
3. Using the property of supplementary angles, we can write the equation as x - angle C = 20.
4. Since angle A and angle C are opposite angles in a cyclic quadrilateral, their sum is 180 degrees.
5. We can write the equation as x + angle C = 180.
6. Now, we have two equations: x - angle C = 20 and x + angle C = 180.
7. Adding these two equations, we get 2x = 200.
8. Dividing both sides by 2, we find x = 100.
9. Therefore, angle A is 100 degrees.

Conclusion:
In cyclic quadrilateral ABCD, if angle A - angle C = 20, then angle A is equal to 100 degrees.

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