Question

Ina cyclic quadrilateral ABCD angle is equal to X + 7 degree and Angle b is equal to Y + 8 degree angle C is equal to 3 Y + 23 degree and Angle d is equal to 4 x + 12 degree find all four angles of cyclic quadrilateral

Answer 1

Answer:

Step-by-step explanation:

The sum of all the angles of the interior angle of a quadrilateral is 360 degrees.

<A = (x+7)°  <B = (y+8)°  <C=(3y +23)°  <D =(4x +12)°

Since we have to solve simultaneously,

We pair up the opposite sides and equal them to 180°.

<A = (x+7)°  &  <C=(3y +23)°

<B = (y+8)° &  <D =(4x +12)°

Now solving simultaneously,

we get,

x+7+3y+23=180°

x+3y+30=180° [180-30]

x+3y=150°·············(i)

y+8+4x+12=180°

y+4x+20=180° [180-20]

y+4x=160°·············(ii)

Now equating the both equations,

x+3y=150°·············(i)

y+4x=160°·············(ii)×3

12x+3y=480·············(ii)

x+3y=150°·············(i)

As solving it the sign changes to minus (-) and 3y gets cancelled,

so, 

11x=330

x=

x=30

Now finding the value of y we get,

We take the equation (i) and put the value of x in order to get the value of y,

x+3y=150

30+3y=150

3y=150-30

3y=120

y=

y=40

Now the angles measures,

<A= (x+7)°= (30+7)° =37°

<B= (y+8)° = (40+8)° =48°

<C= (3y+23)° = (3×40+23)° = (120+23)°= 143°

<D=(4x+12)° = (4×30+12)° =(120+12)° =132