Question

Find the four angles of a cyclic quadrilateral ABCD in which ∠A= (x+y+10)°, ∠B = (y
+20)°, ∠C = (x + y -30)° and ∠D = (x + y)°. ​

Answer 1

Answer: The angles are:

∠A =  110

∠B =  80

∠C = 70

∠D =  100

Step-by-step explanation:

Sum of all angles of a quadrilateral is 360°

∠A+ ∠B + ∠C + ∠D = 360

x+y+10+y+20+x+y-30+x+y = 360

3x+4y = 360... (1)

Also,

Sum of opposite angles of a quadrilateral = 180°

• ∠A + ∠C  = 180

∴ x+y+10+x+y-30 = 180

=> 2x+2y - 20 = 180

=> 2x+2y = 200

=> x + y = 100... (2)

• ∠B  + ∠D = 180

=> y+20+x+y = 180

=> x + 2y +20 = 180

=> x + 2y =  160... (3)

• Now, simultaneous equations are:

3x+4y = 360... (1)

x + y = 100... (2)

x + 2y =  160... (3)

• Subtract equation (2) from (3):

y = 60

• Put y = 60 in eq (2)

x+60 = 100

x = 40

Note: (You can cross check the values in any of the above given equations)

The angles are:

∠A = x + y + 10 = 40+60+10 = 110

∠B = y+20 = 60+20 = 80

∠C = x+y-30 = 40+60-30 = 70

∠D = x+y = 60+40 = 100

Thanks! Please mark me brainliest...