Question

In a quadrilateral interior angles are in ascending order and difference between two consecutive angles is

20°. Then find all the angles.​

Answer 1

$\rm \large\bold{Hola!}$

• GiveN :

→ Let those angles are A, B, C & D

$\mapsto \sf \: \angle \:A- \angle \: B= \angle \: B- \angle \: C= \angle \: C- \angle \: D=20$

$\mapsto \sf\angle A +\angle B+ \angle C+\angle D= 360 \degree</p><p>$

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• To FienD :

→ All the interior angles

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• SolutioN :

$\sf \: \angle A-\angle B =\angle B - \angle C$

$\sf \implies \: 2\angle B = \angle A + \angle C \underline{ \: \: \: \: \: \: \: \: \: \: \: \: }(1)$

Again,

$\sf\angle \: B- \angle \: C= \angle \: C- \angle \:D$

$\sf \implies \: 2\angle \: C = \angle B + \angle D \underline{ \: \: \: \: \: \: \: \: \: \: }(2)$

$\implies \sf\angle \: B + \angle \: C \: = 180 \degree \underline{ \: \: \: \: \: \: \: \: }(3)$

Adding eqn 1 & 2,

$\implies \sf\angle A +\angle B+ \angle C+\angle D= 2( \angle \: B + \angle \: C)$

We know,

$\mapsto \sf\angle \: B - \angle \: C= 20 \degree \underline{ \: \: \: \: \: \: \: \: \: \: }(4)$

Calculating eqn 3 & 4,

$\sf { \underline{\boxed{ \sf{\angle B = 100 }}}}$

and,

$\sf { \underline{\boxed {\sf{\angle C= 80 }}}}$

Hence,

${ \underline{ \boxed{ \sf\angle A = \angle B +20\degree \: = 120 \degree}}}$

and

${ \underline{ \boxed{\sf \: \angle D= \angle C -20\degree = 60 \degree}}}$

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$\therefore { \underline{ \boxed{\sf \: All \: \: the \: \: angles \: \: are \: \: 120 \degree \: , \: 100 \degree \:, \: 80 \degree \: \: and \: \: 60 \degree }}}$

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