Question

If the angles of a quadrilateral are x°, (2x + 13), (3x + 10)° and (x-6)°. Calculate value of x
If the angles of a quadrilateral are in ratio of 2:4:5:7. Calculate the largest and smallest​

Answer 1

Answer:

x + 2x + 13 + 3x+10 + x - 6 = 3600

→ 7x + 17 = 360

→ 7x = 343

→ x = 490

Answer 2

If the angles of a quadrilateral are x°, (2x + 13)°, (3x + 10)° and (x - 6)°, calculate the value of x.

$\:$

Let the angles be :

$\blue{ \pmb{ \sf{ \qquad : \implies \: \angle1 = x \degree}}}$

$\blue{ \pmb{ \sf{ \qquad : \implies \: \angle2 = (2x + 13) \degree }}}$

$\blue{ \pmb{ \sf{ \qquad : \implies \: \angle3 = (3x + 10) \degree }}}$

$\blue{ \pmb{ \sf{ \qquad : \implies \: \angle4 = (x - 6) \degree}}}$

We know that all the angles in a quadrilateral add upto 360°. So :

$\pink{ \pmb{ \sf{ \qquad : \implies \:x \degree + (2x + 13) \degree + (3x + 10) \degree + (x - 6) \degree = 360 \degree }}}$

$\pink{ \pmb{ \sf { \qquad : \implies \:x + 2x + 3x + x + 13 + 10 - 6 = 360}}}$

$\pink{ \pmb{ \sf{ \qquad : \implies \:7x +17 = 360 }}}$

$\pink{ \pmb{ \sf{ \qquad : \implies \:7x = 360 - 17 }}}$

$\pink{ \pmb{ \sf{ \qquad : \implies \: 7x = 343}}}$

$\pink{ \pmb{ \sf{ \qquad : \implies \: x = \cancel \dfrac{343}{7} }}}$

$\pink{ \pmb{ \sf{ \qquad : \implies \: x = 49 }}}$

So, now the angles are :

$\blue{ \pmb{ \sf{ \qquad : \implies \: \angle1 = x \degree = 49 \degree}}}$

$\blue{ \pmb{ \sf{ \qquad : \implies \: \angle2 =(2x + 1 3) \degree = 111 \degree }}}$

$\blue {\pmb{\sf{ \qquad : \implies \: \angle 3 =(3x + 10) \degree = 157 \degree }}} \:$

$\blue{ \pmb{ \sf{ \qquad : \implies \: \angle3 = (x - 6) \degree = 43 \degree }}}$

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If the angles of a quadrilateral are in the ratio of 2:4:5:7, calculate the smallest and largest angle of the quadrilateral.

$\:$

Let the unknown constant be x. So the angles will be :

$\orange{ \pmb{ \sf{ \qquad : \implies \: \angle1 = 2x}}}$

$\orange{ \pmb{ \sf{ \qquad : \implies \: \angle2 = 4x}}}$

$\orange{ \pmb{ \sf{ \qquad : \implies \: \angle 3 = 5x}}}$

$\orange{ \pmb{ \sf{ \qquad : \implies \: \angle4 = 7x }}}$

We know that all the angles in a quadrilateral add upto 360° :

$\purple{ \pmb{ \sf{ \qquad : \implies \: 2x + 4x + 5x + 7x = 360 \degree}}}$

$\purple{ \pmb{ \sf{ \qquad : \implies \: 18x = 360}}}$

$\purple{ \pmb{ \sf{ \qquad : \implies \: x = \cancel \dfrac{360}{18} }}}$

$\purple{ \pmb{ \sf{ \qquad : \implies \:x = 20 }}}$

So, now the angles are :

$\orange{ \pmb{ \sf{ \qquad : \implies \: \angle 1 = 2x = 40 \degree}}}$

$\orange{ \pmb{ \sf{ \qquad : \implies \: \angle2 = 4x = 80 \degree}}}$

$\orange{ \pmb{ \sf{ \qquad : \implies \: \angle 3 = 5x = 100 \degree }}}$

$\orange{ \pmb{ \sf{ \qquad : \implies \: \angle4 = 7x = 140 \degree}}}$

Here, the smallest angle is 40° and largest angle is 140°.

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