In cyclic quadrilateral ABCD, ∠A = 3 ∠C and ∠D = 5 ∠B. Find the measure of each angle of the quadrilateral. - Noon Academy

In cyclic quadrilateral ABCD, ∠A = 3 ∠C and ∠D = 5 ∠B. Find the measure of each angle of the quadrilateral.

Class 10 | Exercise 18C | ICSE | Maths | Selina | Tangents and Intersecting Chords

In cyclic quadrilateral ABCD, ∠A = 3 ∠C and ∠D = 5 ∠B. Find the measure of each angle of the quadrilateral.

Selina Solutions Concise Class 10 Maths Chapter 18 ex. 18(C) - 8

Given, cyclic quadrilateral

$ABCD$

So,

$\angle A\text{ }+\angle C\text{ }=\text{ }{{180}^{o}}~$

[Opposite angles in a cyclic quadrilateral is supplementary]

$3\angle C\text{ }+\angle C\text{ }=\text{ }{{180}^{o}}~$

$~[As\angle A\text{ }=\text{ }3\angle C]$

$\angle C\text{ }=\text{ }{{45}^{o}}$

Now,

$\angle A\text{ }=\text{ }3\angle C\text{ }=\text{ }3\text{ }x\text{ }{{45}^{o}}$

$\angle A\text{ }=\text{ }{{135}^{o}}$

Similarly,

$\angle B\text{ }+\angle D\text{ }=\text{ }{{180}^{o}}$

$[As\angle D\text{ }=\text{ }5\angle B]$

$\angle B\text{ }+\text{ }5\angle B\text{ }=\text{ }{{180}^{o}}$

Or,

$6\angle B\text{ }=\text{ }{{180}^{o}}$

$\angle B\text{ }=\text{ }{{30}^{o}}$

Now,

$\angle D\text{ }=\text{ }5\angle B\text{ }=\text{ }5\text{ }x\text{ }{{30}^{o}}$

$\angle D\text{ }=\text{ }{{150}^{o}}$

Therefore,

$\angle A\text{ }=\text{ }{{135}^{o}},\angle B\text{ }=\text{ }{{30}^{o}},$

$\angle C\text{ }=\text{ }{{45}^{o}},\angle D\text{ }=\text{ }{{150}^{o}}~$

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