Name the angle marked in the diagram.

If $ABC$ is a straight line then value of $x$, in the given diagram will be 

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 $\sec \theta +\mathrm{cosec}\theta$

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

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

The angles of a quadrilateral are in the ratio $3:5:7:9$. Find the measure of each of these angles.

The angles of a quadrilateral are in the ratio $1:2:3:4$. Find the measure of each angle.

In figure, if $\mathrm{segment} \mathrm{PR}=\mathrm{segment} \mathrm{PQ}$, show that $\mathrm{segmenet} \mathrm{PS}>\mathrm{segment} \mathrm{PQ}$.