Question

A quadrilateral ABCD has all its four angles of the same measure. What is the measure of each angle?​

Answer 1

Answer:

90 degrees

Step-by-step explanation:

Lets angles of quadrilateral ABCD be a,b,c and d

According to given condition a=b=c=d

a+b+c+d = 360 (Sum of all angles of a quadrilateral is 360 degrees)

4d = 360 (Since a=b=c=d)

d = 360/4 = 90 degrees

Therefore a=b=c=d = 90 degrees

a = 90, b = 90, c = 90, d = 90

Therefore measure of each angle is 90 degrees

Answer 2

$\red{\underline{\underline{\textsf{\red{Given}}}}}$

$\sf{All\: four \:angles\: are\: same}$

$\red{\underline{\underline{\textsf{\red{To find:}}}}}$

$\sf{The \:measure \:of\: each\: angle}$

$\red{\underline{\underline{\textsf{\red{Concept: }}}}}$

$\small\begin{gathered}\begin{gathered}\\\;\underline{\boxed{\sf\;The\: sum \:of \:the \:angles\: of\: a \:quadrilateral =360^0}}\end{gathered} \end{gathered}$

$\red{\underline{\underline{\textsf{\red{Solution: }}}}}$

$\sf{Let\: the \:one\: angle\: be \:x}$

$\sf{x+x+x+x =360^0}$

$\sf{4x=360^0}$

$\sf{x=90^0}$

$\sf{Hence, \:each \:angle \:is\: equal\: to\: 90^0}$

Answer 3

$\red{\underline{\underline{\textsf{\red{Given}}}}}$

$\sf{All\: four \:angles\: are\: same}$

$\red{\underline{\underline{\textsf{\red{To find:}}}}}$

$\sf{The \:measure \:of\: each\: angle}$

$\red{\underline{\underline{\textsf{\red{Concept: }}}}}$

$\small\begin{gathered}\begin{gathered}\\\;\underline{\boxed{\sf\;The\: sum \:of \:the \:angles\: of\: a \:quadrilateral =360^0}}\end{gathered} \end{gathered}$

$\red{\underline{\underline{\textsf{\red{Solution: }}}}}$

$\sf{Let\: the \:one\: angle\: be \:x}$

$\sf{x+x+x+x =360^0}$

$\sf{4x=360^0}$

$\sf{x=90^0}$

$\sf{Hence, \:each \:angle \:is\: equal\: to\: 90^0}$