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A) $45^\circ $

B) $100^\circ $

C) $180^\circ $

D) $90^\circ $

Answer

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Angle sum property is given by:

\[{\text{A + B + C + D}} = {360^\circ }\]

Let each angle be $x$.

Then according to the angle sum property of vertical angles, the sum of all four angles is equal to \[{360^ \circ }\].

i.e, if A,B,C,D are four vertical angles of two intersecting lines then according to the angle sum property:

$A+B+C+D=360^\circ $

Now here since all four angles are equal therefore,

\[{\text{A = B = C = D = x}}\]

Now , putting in the value of A,B,C,D in the above equation we get:

\[ x + x + x + x = {360^ \circ } \]

On simplifying the above equation,

$\Rightarrow 4x = {360^ \circ } $

On further calculations,

$\Rightarrow x = {90^ \circ } $