Find the fourth angle of a quadrilateral whose angles are $90°, 45°$ and $60°$.

In the given figure, $ABC$ is an isosceles triangle with $AB = AC$. If $AE = AF$ and $\angle BAE=40°$, then the measure of the angle $FEC$ is

In the figure given below, a rectangle of perimeter $76$ units is divided into $7$ congruent rectangles:

What is the perimeter of each of the smaller rectangles?

$5 : 18$ is the ratio of the length and perimeter of a rectangle. What would be the ratio of its length and breadth?

The rod $AC$ of a TV disc antenna is fixed at right angles to the wall $AB$ and a rod $CD$ is supporting the disc as shown in the figure. If $AC=1.5 \mathrm{m}$ long and $CD=3 \mathrm{m}$, find $\sec \theta +\mathrm{cosec}\theta$

What is the area of this trapezoidal garden (All measurements are in cm)? 

1. $60$ sq.cm
2. $180$ sq.cm
3. $210$ sq.cm 
4. $240$ sq.cm

If $\sin \theta =\frac{12}{13}$, find the value of $\cos \theta \& \tan \theta .$

Let $ABCD$ be a square. An arc of a circle with $A$ as centre and $AB$ as radius is drawn inside the square joining the points $B$ and $D$. Points $P$ on $AB, S$ on $AD, Q$ and $R$ on arc $BD$ are taken such that $PQRS$ is a square. Further suppose that $PQ$ and $RS$ are parallel to $AC$. Then, $\frac{\text{ area }PQRS}{\text{ area }ABCD}$ is