Question

One angle of a quadrilateral is 1080 and the remaining three angles are equal. Find The three angles?

Answer 1

$\small\bf{Given}$

One angle of an Quadrilateral is 108°

$\small\bf{To\:Find}$

Ramaining Three angles = ?

$\small\bf{Simplifying:-}$

$\small\bf{Let\:each\: of \:the\: three\: equal\: angles\: be\: x°}\\{\small\bf{Now,\: sum\:of \:angles\: of\: a}}\\{\small\bf{Quadrilateral \:is\:=\: 360°}}$

$\small\bf{108°\:+\: x°\:+ \:x° \:+\: x°\: =\: 360°}$

$\small\bf{ \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:x°\:+ \:x° \:+\: x°\: =\:360°\: - \: 180°}$

$\small\bf{ \:\:\:\:\:\:\:\:\:\: \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:3\:x°\:=\: 252°}$

$\small\bf{ \:\:\:\:\:\:\:\:\:\: \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:x°\:=\:{\small\bf\frac{252°}{3}}}$

$\small\bf{ \:\:\:\:\:\:\:\:\:\: \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:x°\:=\cancel\frac{252°}{3}}$

$\small\bf{ \:\:\:\:\:\:\:\:\:\: \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:x°\:=\:{84°}}$

$\small\bf{Hence\:Each\: of \:the\: three\: equal\: angles}\\{\small\bf{ is\: 84°}}$

.

$\small\bf{\boxed{Thanks}}$

Answer 2

Correct Questions:-

➜One angle of a quadrilateral is 108°and the remaining three angles are equal. Find The three angles?

Given :-

➜ one angle of quadrilateral=108°.

➜And , remaining angles are Equal.

Solution:-

➜Let the remaining angles be =X

➜We know that sum of angles in quadrilateral is 360°.

Therefore,

$108 {}^{o} + x + x + x = 360 {}^{o} \\ \\ 3x = 360 {}^{o} - 108 {}^{0} \\ \\ 3x = 252 {}^{o} \\ \\ x = 252 {}^{o} \div 3 \\ \\ x = 84 {}^{o}$

Hence the remaining angles are 84°.

hope this answer help you...