Question

in the given figure, prove that angle ADC= angle A+B+C

Answer 1

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Answer 2

∠ADC = ∠A + ∠B + ∠C

Step-by-step explanation:

The image of the question is attached below.

Given figure ABCD.

To prove that ∠ADC = ∠A + ∠B + ∠C

Construction: Join BD

By exterior angle property of triangle,

An exterior angle of triangle is equal to the sum of the two opposite interior angles.

In triangle ABD,

∠1 + ∠2 = ∠5 ----------- (1)

Similarly in triangle CBD,

∠4 + ∠3 = ∠6 ----------- (2)

Adding equation (1) and (2), we get

∠1 + ∠2 + ∠4 + ∠3 = ∠5 + ∠6

⇒ ∠1 + (∠2 + ∠3) + ∠4 = ∠ADC (using figure)

⇒ ∠A + ∠B + ∠C = ∠ADC

Switch the sides.

∠ADC = ∠A + ∠B + ∠C

Hence proved.

To learn more...

1. In the given figure AD=BC and angle ADC = angle BCD.

Prove that AC =BD

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2. In the given figure, ABCD is a quadrilateral in which AB || CD and AD || BC.Prove that angle ADC = angle ABC​

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