Acute and obtuse angles

An angle which is more than 180∘180∘ and less than 360∘360∘ is called reflex angle.

An angle which is more than  $\displaystyle 180^{0}$ and less than $\displaystyle 360^{0}$ is called reflex angle.

Angle formed at a point is $\displaystyle { 360 }^{ o }$. 

Obtuse angle ranges from $\displaystyle { 90 }^{ o }$ to $\displaystyle { 180 }^{ o }$
So, sum of least obtuse angle is $\displaystyle { 91 }^{ o }+{ 91 }^{ o }={ 182 }^{ o }$ which is a reflex angle.
Sum of maximum obtuse angle is $\displaystyle { 179 }^{ o }+{ 179 }^{ o }={ 358 }^{ o }$ which is a reflex angle.

Reflex angle must be between $\displaystyle { 180 }^{ o }$ and $\displaystyle { 360 }^{ o }$. It can't be equal to $\displaystyle { 180 }^{ o }$ or $\displaystyle { 360 }^{ o }$ as these are straight and complete angle respectively.

An angle is said to be a reflex angle if it measures more than $180^o$ but less that $360^o$.

The law of reflection states that the angle of incidence equals the angle of reflection. Using the formula for the angle between lines with slopes m1 and m2, tan(theta) = |(m2-m1)/(1+m1m2)|. Setting the angle of the incident ray equal to the reflected ray relative to the mirror slope, the resulting slope is 1.

Let the angles of the triangle be $2x,3x, 4x$. 

An angle which measures $ {0}^{o} $ is called zero angle.

an angle which measures 0 degree is called a zero angle..

$\displaystyle \because $ PQ = PR 
$\displaystyle \Rightarrow $ $\displaystyle \angle Q=\angle R$
Given that $\displaystyle \angle Q=2\angle P$
We have
$\displaystyle \angle P+\angle Q+\angle R=180^{\circ}$
$\displaystyle \frac{\angle Q}{2}+\angle Q+\angle Q=180^{\circ}$
$\displaystyle \frac{5}{2}\angle Q=180^{\circ}$
$\displaystyle \angle Q=72^{\circ}$        

Line  $3x+2y=6$

We know that the complement angle

We know that the complement angle

Let the angle be $x^0$.

Let the angle be $x^0$.

Let the angle be $x^0$.

We know that the supplement angle

We know that the supplement angle

We know that the complement angle

We know that the sum of the supplement angles

We know that the complement angle

Let the angle be $x^0$.

We know that the complement angle

Let the angles be $3x$ and $2x$.

Sum of complementary angles is $90^{\circ}$

Complete angle $=360^{\circ}$

1. Right angle $=90^{\circ}$
   
   
   2. Straight angle $=180^{\circ}$
   
   
   3. Reflex angle lies between $180^{\circ}$ and $360^{\circ}$
   
   
   So the descending order of angles is
   $2>1>3$

Le the angles be $x,3x$ and $2x$

Let the two supplementary angles are $x^{\circ}$ and
$180^{\circ} - x$
By hypothesis, $x - (180^{\circ} - x) = 40^{\circ}$
or $2x - 180^{\circ} = 40^{\circ}$
or  $2x = 220^{\circ}$
or    $x = 110^{\circ}$

Given trignometric equations are:

Given: $\cfrac { 1 }{ a+c } +\cfrac { 1 }{ b+c } =\cfrac { 3 }{ a+b+c } $

Given that $ A:B:C = 1:5:6 $

For two triangles to be similar by SAS similarity, the included angle between the proportional sides must be equal. Given AB/DE = BC/FD, the included angles are angle B and angle D, so angle B must equal angle D.

(I) We draw a triangle POR with $\quad \angle RPO={ 120 }^{ O }.\quad $

Trisected angle $\displaystyle =\frac{162^{\circ}}{3}=54^{\circ}$

An angle which measure $0^0$ is called zero angle.

We know that the supplement angle