Question

Quadrilateral XYZW is a cyclic quadrilateral .If m∠Y=(3x +5)° ,m∠W= (2x -25)° then find value of x also find measures of ∠W and ∠Y.​

Answer 1

Sum of opposite angles of a cyclic quadrilateral = 180°

Which means :-

$= m∠y + m∠w = 180°$

$= 3x + 5 + 2x - 25 = 180$

$= 3x + 2x + 5 + ( - 25) = 180$

$= 5x + ( - 20) = 180$

$= 5x - 20 = 180$

$= 5x = 180 + 20$

$= 5x = 200$

$= x = \frac{200}{5}$

$\color{olive}x \color{plum}=\color{hotpink} 40$

Then :-

m∠y =

$= 3 \times 40 + 5$

$= 120 + 5$

$\color{olive}m∠y = \color{hotpink}125°$

m∠w =

$= 2 \times 40 - 25$

$= 80 - 25$

$\color{olive}m∠w = \color{hotpink}55°$

As the value of both the angles are adding up to form 180° (125+55=180), we can conclude that we have found out the correct value of x .

Therefore , the value of x = 40 , and m∠y = 125° , m∠w = 55° .

Answer 2

Step-by-step explanation:

Sum of opposite angles of a cyclic quadrilateral = 180°

Which means :-

= m∠y + m∠w = 180°=m∠y+m∠w=180°

= 3x + 5 + 2x - 25 = 180=3x+5+2x−25=180

= 3x + 2x + 5 + ( - 25) = 180=3x+2x+5+(−25)=180

= 5x + ( - 20) = 180=5x+(−20)=180

= 5x - 20 = 180=5x−20=180

= 5x = 180 + 20=5x=180+20

= 5x = 200=5x=200

= x = \frac{200}{5}=x=

5

200

\color{olive}x \color{plum}=\color{hotpink} 40x=40

Then :-

m∠y =

= 3 \times 40 + 5=3×40+5

= 120 + 5=120+5

\color{olive}m∠y = \color{hotpink}125°m∠y=125°

m∠w =

= 2 \times 40 - 25=2×40−25

= 80 - 25=80−25

\color{olive}m∠w = \color{hotpink}55°m∠w=55°

As the value of both the angles are adding up to form 180° (125+55=180), we can conclude that we have found out the correct value of x .

Therefore , the value of x = 40 , and m∠y = 125° , m∠w = 55° .