Question

the angle of a quadrilateral are(2 X + 3)°,(x+7)°,(3x-5)°,(2x+11)°. find the measure of each angle of the quadrilateral.​

Answer 1

Answer:

Sum of all angles of quadrilateral = 360°

$\: \: \: \: \: (2x + 3) + (x + 7) +( 3x - 5) \\ \: \: \: \: \: \: + (2x + 11) = 360 \\ = > 2x + 3 + x + 7 + 3x - 5 + \\ \: \: \: \: \: \: \: \: 2x + 11 = 360 \\ = > 8x + 16 = 360 \\ = > 8x =3 60 - 16 \\ = > 8x = 344 \\ = > x = \frac{344}{8} \\ = > x = 43$

First angle

$= (2 \times 43 + 3)°= 89°$

Second angle

$(43 + 7)° = 50°$

Third angle

$= (3 \times 43 - 5)° = 124°$

Fourth angle

$(2 \times 43 + 11) ° = 97 °$

Answer 2

$\huge{\star}{\underline{\boxed{\red{\sf{Answer :}}}}}{\star}$

★ Given :-

Angles of a quadrilateral are :-

• (2x + 3)°

• (x + 7)°

• (3x - 5)°

• (2x + 11)°

===========================

★ To Find :-

Sides of the quadrilateral

==========================

★ Solution :-

We know that,

Sum of all angles of quadrilateral = 360°

__________[Put Values]

(2x + 3)° + (x + 7)° + (3x - 5)° + (2x + 11)° = 360°

2x + 3 + x + 7 + 3x - 5 + 2x + 11 = 360

8x + 16 = 360

8x = 360 - 16

8x = 344

x = 344/8

x = 43°

__________________

Angles of a quadrilateral are :-

• (2x + 3)° = 2(43) + 3 = 89°

• (x + 7)° = 43 + 7 = 50°

• (3x - 5)° = 3(43) - 5 = 124°

• (2x + 11)° = 2(43) + 11 = 97°

$\rule{400}{4}$

$\huge{\star}{\underline{\boxed{\blue{\sf{Verification}}}}}{\star}$

Add all the angles and then put them equal to the 360.

A.T.Q

89 + 50 + 124 + 97 = 360

139 + 221 = 360

360° = 360°

R.H.S = L.H.S

$\huge{\boxed{\green{\sf{Hence \: Verified}}}}$