Question

In a cyclic quadrilateral ABCD, 2 A= 4 LC & LB 34D, then find all the angles of ABCD.
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Answer 1

Answer:

∠A = 144°

∠B = 135°

∠C = 36°

∠D = 45°

Step-by-step explanation:

First, we know that the opposite angles of a cyclic quadrilateral add to 180°

So, ∠A + ∠C = 180°

or, 4∠C + ∠C = 180°

Or, 5∠C = 180°

So, ∠C = 36°                      (ANS,i)

And, then ∠A will be:

A = 4∠C = 4 × 36°, or, 144°   (ANS,ii)

Then,

∠B + ∠D = 180°

or, 3∠D + ∠D = 180°

or, 4∠D = 180°

So, ∠D = 45°                     (ANS,iii)

And, then ∠B will be:

∠B= 3∠D = 3 × 45°, or, 135°   (ANS,iv)

So, all the angles are:

∠A = 144°, ∠B = 135°, ∠C = 36°, ∠D = 45°

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