Question

in cyclic quadrilateral ABCD angle A - angle C = 20 degree, then find angle A. plz give me with full explanation and ans is 100 degree

Answer 1

A = 100°

C = 80°

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Verification :

$a \: - \: c \: = \: 20$

$100 \: - \: 80 \: = \: 20$

$20 = 20$

Answer 2

∠A = 100°

Given :

In cyclic quadrilateral ABCD , ∠A - ∠C = 20°

To find :

The measure of ∠A

Solution :

Step 1 of 2 :

Form the equation to measure of ∠A

In a cyclic quadrilateral ABCD

∠A - ∠C = 20° - - - - - - (1)

Again we know that the sum of the opposite angles of a cyclic quadrilateral is 180°

∠A + ∠C = 180° - - - - - - (2)

Step 2 of 2 :

Find measure of ∠A

∠A - ∠C = 20° - - - - - - (1)

∠A + ∠C = 180° - - - - - - (2)

Adding Equation 1 and Equation 2 we get

2∠A = 200°

⇒ ∠A = 100°

Putting ∠A = 100° in Equation 2 we get

100° + ∠C = 180°

⇒ ∠C = 180° - 100°

⇒ ∠C = 80°

Hence measure of ∠A = 80°

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