Question

the four angle of a quadrilateral are x°,(x-10)°,(x+30)° and 2x°. Find all the angles of quadrilateral and also write the greatest angle​

Answer 1

❍ The angles of the Quadrilateral are x°, (x – 10)°, (x + 30)° and 2x° respectively.

⠀⠀⠀$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

• The sum of all angles of the Quadrilateral is 360°. Therefore,

$:\implies\sf x + (x - 10)^\circ + (x + 30)^\circ + 2x = 360^\circ \\\\\\:\implies\sf x + x + x + 2x - 10 + 30 = 360^\circ \\\\\\:\implies\sf 3x + 2x - 10 + 30= 360^\circ \\\\\\:\implies\sf 5x + 20 = 360^\circ \\\\\\:\implies\sf 5x = 360^\circ - 20 \\\\\\:\implies\sf 5x = 340^\circ \\\\\\:\implies\sf x = \cancel\dfrac{340^\circ}{5} \\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 68^\circ}}}}}\;\bigstar$

Hence,

• First angle, x = 68°
• Second angle, (x - 10)° = (68 - 10)° = 58°
• Third angle, (x + 30)° = (68 + 30)° = 98°
• Fourth angle, 2x = 2(68)° = 136°

$\therefore{\underline{\sf{Hence, the\;greatest\;angle\;is\;\bf{136^\circ }.}}}$

━━━━━━━━━━━━━━━━━━━⠀⠀⠀

⠀

V E R I F I C A T I O N :

• As we know that sum of the all angles of Quadrilateral is 360°. And, we've measure of each angle. So, Let's verify :

$\dashrightarrow\sf a + b + c + d = 360^\circ \\\\\\\dashrightarrow\sf 68^\circ + 58^\circ + 98^\circ + 136^\circ = 360^\circ \\\\\\\dashrightarrow{\boxed{\underline{\sf{360^\circ = 360^\circ}}}}$

$\therefore{\underline{\textsf{\textbf{Hence Verified!}}}}$

Answer 2

Step-by-step explanation:

$\underline{\underline{\maltese\: \: \textbf{\textsf{Question}}}}$

• The four angle of a quadrilateral are x°, (x - 10)°, (x + 30)° and 2x°. Find all the angles of quadrilateral and also write the greatest angle.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Answer}}}}$

• Our required angles are 68°, 58°, 98°, and 136°. And the greatest angles is 136°.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Given}}}}$

• The four angle of a quadrilateral are x°, (x - 10)°, (x + 30)° and 2x°.

$\underline{\underline{\maltese\: \: \textbf{\textsf{To\ Find}}}}$

• We have to find out all the angles of quadilateral. Also, we have to write the greatest angle.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Basic\ Terms}}}}$

• Quadrilateral : A quadrilateral is a polygon in Euclidean plane geometry with four edges and four vertices.
• Angle : An angle is a combination of two rays (half-lines) with a common endpoint.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Solution}}}}$

• As per the given information, we know that the known values are the measure of all the four angles of quadilateral.
• Then firstly, by using the angles sum property of quadilateral we will find out the value of x.
• After, that by applying the value of x in the given angles we will find out the angles of quadilateral.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Calculations}}}}$

We know that :-

${\underline{\boxed{\sf {Sum\ of\ all\ angles\ of\ quadilateral\ =\ 360^{\circ}.}}}}$

By applying the values, we get :-

$\sf \mapsto {x\ +\ (x\ -\ 10)^{\circ}\ +\ (x\ +\ 30)^{\circ}\ +\ 2x\ =\ 360^{\circ}}$

$\sf \mapsto {x\ +\ x\ +\ x\ +\ 2x\ -\ 10\ +\ 30\ =\ 360^{\circ}}$

$\sf \mapsto {3x\ +\ 2x\ -\ 10\ +\ 30\ =\ 360^{\circ}}$

$\sf \mapsto {5x\ +\ 20\ =\ 360^{\circ}}$

$\sf \mapsto {5x\ =\ 360^{\circ}\ -\ 20}$

$\sf \mapsto {5x\ =\ 340^{\circ}}$

$\sf \mapsto {x\ =\ \cancel \dfrac{340^{\circ}}{5}}$

${\therefore{\underline{\boxed{\tt {x\ =\ 68^{\circ}.}}}}}$

• Now, we have the value of x. So, now we will find out the angles of quadilateral and the greatest angle.

➊ 1st angle = x = 68°.

➋ 2nd angle = (x - 10)° = (68 - 10)° = 58°.

➌ 3rd angle = (x + 30)° = (68 + 30)° = 98°.

➍ 4th angle = 2x = 2(68)° = 136°.

${\therefore{\underline{\sf{\pmb{Hence,\ greatest\ angle\ of\ quadilateral\ =\ 136^{\circ}.}}}}}$