Question

$\huge\underline\bold\red{Question}$

if 3 angles of a quadrilateral are 100 degree, 75 degree and 105 degree then the measurement of fourth angle is ???
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Answer 1

$\huge{\underline{\mathcal{\red{A}\green{n}\pink{s}\orange{w}\blue{e}\pink{R:-}}}}$

$\rule{200px}{.3ex}$

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

The angles are:-

100°, 75°, and 105° .

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

The fourth angle = ?

$\large\underline\bold\red{Solution:-}$

As We Know :- The sum of four angles of a quadrateral = 360°

Now let the unknown angle be = x

Then,

100° + 75° + 105° + x = 360°

$\implies$ 175° + 105° + x = 360°

$\implies$ 280° + x = 360°

$\implies$ x = 360° - 280°

$\implies$ x = 80°

$\therefore\large\underline\bold\red{The\:Forth\:Angle\:is\:80°}$

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$\large\underline\bold\red{Properties\:of\:Quadrilateral:-}$

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Answer 2

Answer:

Given :-

• Three angles of a quadrilateral are 100 degree, 75 degree and 105 degree.

To Find :-

• What is the measurement of the fourth angles.

Solution :-

Let,

$\mapsto$ Fourth angle of a quadrilateral be x

As we know that :

$\bigstar \: \sf\boxed{\bold{\pink{Sum\: of\: four\: angle\: of\: quadrilateral =\: 360^{\circ}}}}$

According to the question by using the formula we get,

$\longrightarrow \sf 100^{\circ} + 75^{\circ} + 105^{\circ} + x =\: 360^{\circ}$

$\longrightarrow \sf 175^{\circ} + 105^{\circ} + x =\: 360^{\circ}$

$\longrightarrow \sf 280^{\circ} + x =\: 360^{\circ}$

$\longrightarrow \sf x =\: 360^{\circ} - 280^{\circ}$

$\longrightarrow \sf\bold{\red{x =\: 80^{\circ}}}$

$\therefore$ The measurement of fourth angle is 80°.

VERIFICATION :-

$\implies \sf 100^{\circ} + 75^{\circ} + 105^{\circ} + x =\: 360^{\circ}$

By putting x = 80° we get,

$\implies \sf 100^{\circ} + 75^{\circ} + 105^{\circ} + 80^{\circ} =\: 360^{\circ}$

$\implies \sf\bold{\purple{360^{\circ} =\: 360^{\circ}}}$

Hence, Verified.