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 $\sec \theta +\mathrm{cosec}\theta$

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

In the adjacent figure, the bisectors of $\angle A$ and $\angle B$ meet in a point $P$. If $\angle C=100°$ and $\angle D=60°$, find the measure of $\angle APB$.

Prove that the sum of the angles of a quadrilateral is $360°$.

The three angles of a quadrilateral are $76°, 54° \mathrm{and} 108°$. Find the measure of the fourth angle.

Three angles of a quadrilateral are equal and the measure of the fourth angle is $120°$. Find the measure of each of the equal angles.

Two angles of a quadrilateral measure $85°$ and $75°$ respectively. The other two angles are equal. Find the measure of each of these equal angles.

$\mathrm{A}\mathrm{B}$ and $\mathrm{C}\mathrm{D}$ are respectively the smallest and longest sides of a quadrilateral $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ as shown in figure. Show that $\mathrm{\angle }\mathrm{A}>\mathrm{\angle }\mathrm{C}$ and $\mathrm{\angle }\mathrm{B}>\mathrm{\angle }\mathrm{D}.$

In shown figure, $\mathrm{P}\mathrm{R}>\mathrm{P}\mathrm{Q}$ and $\mathrm{P}\mathrm{S}$ bisects $\mathrm{\angle }\mathrm{Q}\mathrm{P}\mathrm{R}.$ Prove that $\mathrm{\angle }\mathrm{P}\mathrm{S}\mathrm{R}>\mathrm{\angle }\mathrm{P}\mathrm{S}\mathrm{Q}.$

The angles of a quadrilateral are respectively $120°$, $75°$ and $135°$, the measure of fourth angle is:

Which of the following statement is true?