There are three angles, The second angle is one-third of the compliment of the first angle. The third angle is half of the supplement of the first angle. The third angle is $6$ times the second angle. Find the first angle.

In the given figure, the angles $a, b, c, d \& e$ are consecutive integers in degree. $a=$_____.

In the given figure, $DAE\parallel BC, \angle BAD=\left(2x-70\right)°, \angle ACB=\left(x-20\right)° \& \angle FAG=\left(2x+20\right)°$ find $\angle EAC$.

In a quadrialteral $ABCD, \angle A:\angle B:\angle C:\angle D=3:4:5:6$, then $ABCD$ is a _____. 

$PQR \& XYZ$ are triangles. The perimeter of each triangle is $12 cm$. $PQR$ is an equilateral. $XY=4 cm \& YZ=ZX$. Both the triangles are _____.

In a $△ABC, \angle A=\angle B+\angle C. O \& S$ are the orthocentre and the circumcenter of $△ABC$. If $AB=12 cm \& AC=5 cm$, then find the distance between $O \& S$.

$ABC \& DEF$ are triangles. Consider the following:

$1. \angle A=40° , \angle B=60°, \angle C=80°, AB=5 cm \& BC=6 cm$

$2.\angle D=\angle F, \angle E=80°, DF=6 cm, \& EF=8 cm$

Which of the following can be concluded? 

$A$ is an obtuse angle. The measure of $\angle A$ and twice its supplement differ by $30°$. Then $\angle A$ can be

In the figure below, $2\angle P=\angle QOR. OQ \& OR$ are the bisectors of $\angle Q \& \angle R$ respectively. Find $\angle P$.