Question

An interior angle of a hexagon are (2x+17),(3x-25),(2x+49),(x+40),(4x-17),(3x-4)
Find the value of x
Find smallest interior angle of the quadrilateral
Find the largest interior angle of the
quadrilateral
Find the largest exterior angle of the quadrilateral

Answer 1

Answer:

(2x+17)+(3x-25)+(2x+49)+(x+40)+(4x-17)+(3x-4)=720

=2x+3x+2x+x+4x+3x+17-25+49+40-17-4=720

=15x+60=720

=15x=660

=x=660/15=44

Answer 2

GIVEN:

• The interior angles of a hexagon are (2x+17),(3x-25),(2x+49),(x+40),(4x-17),(3x-4)

TO FIND:

• What is the value of x ?
• What is the smallest interior angle of the quadrilateral ?
• What is the largest interior angle of the quadrilateral ?

SOLUTION:

We have given that, the interior angles of a hexagon are (2x+17),(3x-25),(2x+49),(x+40),(4x-17),(3x-4)

We know that the sum of all angles of a hexagon is 720°

According to question:-

$\rm{ (2x+17)+(3x-25)+(2x+49)+(x+40)+(4x-17)+(3x-4) = 720}$

$\rm{ 2x+17+3x-25+2x+49+x+40+4x-17+3x-4 = 720}$

$\rm{\rightharpoonup 15x + 60 = 720}$

$\rm{\rightharpoonup 15x = 720 - 60}$

$\rm{\rightharpoonup 15x = 660}$

$\rm{\rightharpoonup x = \large\frac{660}{15}}$

$\large\bf{\star \: x = 44\: \star}$

❛ The value of x is 44 ❜

✬ Measure of angles ✬

➨ $\rm{2 \times 44+17 = 105°}$

➨ $\rm{<strong> </strong>3 \times 44 -25 = 107°}$

➨ $\rm{2 \times 44 +49 = 137°}$

➨ $\rm{ 44 + 40 = 84°}$

➨ $\rm{4 \times 44 -17 = 159°}$

➨ $\rm{ 3 \times 44 -4 = 128°}$

VERIFICATION:

The sum of all angles should be 720°

➩ $\rm{ 105+107+137+84+159+128 = 720}$

➩ $\rm{ 720° = 720° }$

[L.H.S. = R.H.S.]

VERIFIED...

➲ The smallest interior angle of the quadrilateral = 84°

➲ The largest interior angle of the quadrilateral = 159°

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