Question

Find x

I need a complete solution and answer

ty in advance

Answer 1

$\bold{\huge{\underline{ Solution }}}$

Given :-

• Here, we have four exterior angles of the quadrilateral that is 9x° , 4x° , (5x - 10)° , (5x + 25)°

To Find :-

• We have to find the measurement of all the exterior angles

Let's Begin :-

Here, we have

• Angle ABD = 9x°
• Angle CDB = 4x°
• Angle HGE = (5x - 10)°
• Angle DEG = ( 5x + 25)°

We know that,

• Sum of interior angle and exterior angle is equal to 180°

Therefore,

Interior angles of the given quadrilateral

• Angle B= 180° - 9x°
• Angle D = 180° - 4x°
• Angle E = 180° - ( 5x + 25)°
• Angle G = 180° - ( 5x - 10)°

We also know that,

• The sum of angles of quadrilateral is 360°

That is,

$\bold{ {\angle} B + {\angle } D + {\angle} E + {\angle } G = 360{\degree} }$

Subsitute the required values,

$\sf{ ( 180 - 9x){\degree} + (180 - 4x){\degree} + (180 - (5x + 25)){\degree} + (180 - (5x - 10){\degree} = 360{\degree}}$

$\sf{ 180 - 9x + 180 - 4x + 180 - 5x - 25 + 180 - 5x + 10 = 360{\degree}}$

$\sf{ 180 + 180 + 180 + 180 - 9x - 4x - 5x - 5x -25 + 10 = 360{\degree}}$

$\sf{ 720 - 23x - 15 = 360{\degree}}$

$\sf{ 705 - 23x = 360{\degree}}$

$\sf{ 705 - 360 = 23x }$

$\sf{ 23x = 345 }$

$\sf{ x = }{\sf{\dfrac{ 345}{25}}}$

$\sf{ x = }{\sf{\cancel{\dfrac{ 345}{25}}}}$

$\bold{ x = 15 }$

Thus, The value of x is 15°

Therefore,

All the exterior angles of the given quadrilateral are :-

Angle ABD

$\sf{ = 9(15) }$

$\bold{ = 135{\degree}}$

Angle CDB

$\sf{ = 4(15) }$

$\bold{ = 60{\degree}}$

Angle HGE

$\sf{ = 5(15) - 10 }$

$\sf{ = 75 - 10 }$

$\bold{ = 65 {\degree}}$

Angle DEG

$\sf{ = 5(15) + 25 }$

$\sf{ = 75 + 25 }$

$\bold{ = 100 {\degree}}$

Hence, All the exterior angles of the given quadrilateral are 135° , 60° , 65° and 100°