Question

quadrilateral has three acute angles. If each measures 75°, then what is the measure of fourth angle?

Answer 1

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${ \bold { \underline{\large{Question : - }}}} \:$

Quadrilateral has three acute angles. If each measures 75° , then what is the measure of fourth angle ?

${ \bold { \underline{\large{Given : - }}}} \:$

Measure of three angles of quadrilateral 75°.

${ \bold { \underline{\large{To \: Find : - }}}} \:$

Measure of not given angle of quadrilateral.

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$\large\boxed{\boxed{\tt{So\:let's \:do\:it\::-}}}$

Let not given angle = ∠1

Sum of all angles of quadrilateral = 360°

SO,

75° + 75° + 75° + ∠1 = 360°

225° + ∠1 = 360°

∠1 = 360° - 225°

∠1 = 135°

∴ Measure of not given angle of the quadrilateral is 135°.

$\sf{\green \dag \underbrace{Verification}}\green \dag$

75° + 75° + 75° + 135° = 360°

225° + 135° = 360°

360° = 360°

H E N C Eㅤ V E R I F I E D

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Answer 2

$\large{\boxed{\boxed{\sf{firstly,~ let~ understand~ the~ concept~ used:-}}}}$

Here is a quadrilateral which has three acute angles. And sum of each angles is 75°. We have to take fourth angle be ∠1.

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★ Let's do it:-

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Given:-

• Measure of three acute angles is 75°.

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To find:-

• Measure of fourth angle?

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Solution:-

Let the fourth angle be ∠1.

★ We know that:-

$\star{\boxed{\sf{\orange{Sum~ of~ all~ angles~ of~ quadrilateral = 360°}}}}$

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Therefore,

$\large{\tt{\longmapsto{75° + 75° + 75° + ∠1 = 360°}}}$

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$\large{\tt{\longmapsto{225° + ∠1 = 360°}}}$

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$\large{\tt{\longmapsto{∠1 = 360° - 225°}}}$

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$\large{\tt{\longmapsto{∠1 = 135°}}}$

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Hence, the measure of fourth angle is 135°.

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