Question

Express in radians, degrees the fourth angle of quadrilateral which has three angles 46° 30 ' 10 " , 75° 44' 45" , 123 degrees 9 minutes 35 seconds
$( \: take \ \pi = 335 \div 113 )$
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Answer 1

Answer with explanation:

⇒1 Degree= 60 minute =3600 seconds

By Angle sum property of Quadrilateral

The Sum of four angles of Quadrilateral is 360°.

⇒46° 30' 10" + 75° 44' 45"+123° 9' 35"+Fourth Angle =360°

⇒244° 83' 90" +Fourth Angle =360°

⇒244° 84' 30"+Fourth Angle =360°

Fourth Angle = 360° - 245° 24'30"

Fourth Angle =359°60' - 245° 24'30"

Fourth Angle =359°59'60" - 245° 24'30"

                      =114° 25' 30"

   $=114^{\circ} 25' [\frac{1}{2}]'\\\\=114^{\circ} [\frac{51}{2}]'\\\\=114^{\circ} [\frac{51}{120}]^{\circ} \\\\=[\frac{114 \times 40 +17}{40}]^{\circ}\\\\=[114\frac{17}{40}]^{\circ}$

Also, 360° =2 π Radians

  $1^{\circ}=\frac{\pi{\text{Radian}}}{180}$

   $[114\frac{17}{40}]^{\circ}=\frac{114.425 \times\pi }{180}\\\\=\frac{114.425}{180}\times \frac{335}{113}\\\\=\frac{38332.375}{20340}\\\\=1.885 \text{Radian}$

Answer 2

Answer:

answer is 2

Step-by-step explanation:

Given  :-

Express in Radian the fourth angle of a quadrilateral which has three angles 46 degree 30 minutes 10 seconds 75 degree 44 minutes 45 seconds and 123

Now the sum of three given angles will be

46° 30´ 10” + 75°44´45” + 123°9´35”

Since 90 degree = 1’30” and 84’ = 1 degree 24”

We get 245 degree 24’30”

Now the sum of all the angles of a quadrilateral is 360 degree.

So fourth angle will be 360 – (245°24’30”)  

Since 360° = 359 degree 59’60” we get 114°35’30”

Now we need to convert it into radians

114 degree 35’30” = 114° + (35 + 30/60)’

= 114 degree(71/120)’ = 114 degree + 71/120 degree

=  (13751 / 120) degree

Since 180° = π radians

13751/120 x π/180 radians

= 13751/120 x 1/180 x 355/113

= 4881605 / 2440800

= 2 Radians