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In a cyclic quadrilateral abcd

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

Find all four angles

1
by Rajanverma

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

Find all four angles

by Rajanverma

Log in to add a comment

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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°

To verify,

Add all the angles to get 360°

THANK YOU

<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°

To verify,

Add all the angles to get 360°

THANK YOU