Question

4.Three angles of a quadrilateral are equal and the fourth angle is equal to 144°.Findeach

of the equal angles of the quadrilateral​

Answer 1

Given

• Three angles of a quadrilateral are equal.
• Fourth angle of the quadrilateral is 144°.

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To find

• Each of the equal angles of the quadrilateral.

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Solution

• We have the fourth angle = 144°.

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★ As given in the question, three angles are equal.

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• Let each angle of the equal angles be x.

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{We\: know\: that}}}$

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$\bigstar{\boxed{\boxed{\bf{Angle\: sum\: property_{(Quadrilateral)} = 360^{\circ}}}}}$

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• According to the question

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$\tt:\implies\: \: \: \: \: \: \: \: {x + x + x + 144 = 360}$

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$\tt:\implies\: \: \: \: \: \: \: \: {3x + 144 = 360}$

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$\tt:\implies\: \: \: \: \: \: \: \: {3x = 360 - 144}$

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$\tt:\implies\: \: \: \: \: \: \: \: {3x = 216}$

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$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{216}{3}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {\underline{\boxed{\purple{x = 72^{\circ}}}}}$

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Hence,

• Each of the equal angles of the quadrilateral is 72°.

Answer 2

Question:-

Three angles of a quadrilateral are equal and the fourth angle is equal to 144°.Find each of the equal angles of the qquadrilateral.

Answer:-

• The equal angle of quadrilateral is 72°

To find:-

• Each equal angle of quadrilateral

Solution:-

• Fourth angle = 144°
• Three angles of quadrilateral are equal

Let,

• The three angles = x

As we know,

$\boxed{ \mathfrak{ \Large{ sum \: of \: all \: angles \: of \: quadrilateral = 360 \degree}}}$

According to question,

$\Large {\sf: \implies \: \: \: \: \: \: \: x + x + x + 144 = 360 \degree}$

$\Large {\sf: \implies \: \: \: \: \: \: \: 3x + 144 = 360 \degree}$

$\Large {\sf: \implies \: \: \: \: \: \: \: 3x = 360 - 144}$

$\Large {\sf: \implies \: \: \: \: \: \: \: 3x = 216 \degree}$

$\Large {\sf: \implies \: \: \: \: \: \: \: x = \frac{216}{3} }$

$\Large {\sf: \implies \: \: \: \: \: \: \: x = 72 \degree}$

Hence,

The equal angle of quadrilateral is 72°