Quadrilaterals ...

Two angles of a quadrilateral are $$68^{\circ}$$ and $$76^{\circ}$$. If the other two angles are in the ratio $$5 : 7$$, find the measure of largest of them.

$$ P,Q, R $$ and $$ S $$ are the mid-points of sides $$ AB, BC, CD $$ and $$ DA $$ respectively of rhombus $$ ABCD $$. Quadrilateral $$ PQRS $$ is a rectangle. Under what condition will $$ PQRS $$ be a square ?

In triangle $$ ABC $$, $$ M $$ is mid-point of $$ AB $$ and a straight line through $$ M $$ and parallel to $$ BC $$ cuts $$ AC $$ in $$ N $$. Find the lenghts of $$ AN $$ and $$ MN $$ if $$ BC= 7 $$ cm and $$ AC= 5 $$ cm.

Two angles of a quadrilateral are $$89^{\circ}$$ and $$113^{\circ}$$. If the other two angles are equal, find the equal angles.

In the given figure:
$$\angle b = 2a + 15^{\circ}$$ and $$\angle c = 3a + 5^{\circ}$$, find the value of $$\angle b $$.

Three angles of a quadrilateral are equal. If the fourth angle is $$69^{\circ}$$, find the measure of equal angles.

Angles of a quadrilateral are $$(4x)^{\circ},\ 5(x + 2)^{\circ},\ (7x - 20)^{\circ}$$ and $$6(x + 3)^{\circ}$$. Find the value of $$x$$ (in degrees).

From the following figure, find $$x$$.

Find $$\angle ACD$$.

Angles of a quadrilateral are $$(4x)^{\circ}, 5(x + 2)^{\circ}, (7x - 20)^{\circ}$$ and $$6(x + 3)^{\circ}$$. Find the smallest angle of the quadrilateral.