Answer Should be Correct and Answer Should not be copied from any website . Math Question Linear Equation in Two Variables. Correct answer is mark as brainliest
The Question is
(1) Find the four angles of a cyclic Quadrilateral ABCD in which Angle A = (2x -1)° , Angle B = (y+5)° Angle C = (2y+15)° and Angle D = (4x -7)°.
Answers
Solution:-
As we know that sum of opposite angles of Cyclic Quadrilateral is 180°.
In the given Cyclic Quadrilateral ABCD , ∠A & ∠C and ∠B & ∠D forms pair of opposite angles.
Now,
→ ∠A + ∠C= 180°
Substitute the value we get
→ 2x - 1 + 2y +15 = 180°
→ 2x +2y +14 = 180°
→ 2x + 2y = 180-14
→ 2x + 2y = 166°
taking Common 2
→ x + y = 83° ..............................(i)
And ,
→ ∠B+ ∠D = 180°
→ y+5 + 4x -7 = 180°
→ 4x +y -2 = 180°
→ 4x + y = 180+2
→ 4x +y = 182° .....................(ii)
Subtracting equation (i) from equation (ii) ,we obtain
→ 4x - x + y-y = 182-83
→ 3x = 99
→ x = 99/3
→ x = 33
Therefore, x = 33°
Substituting x = 33 in equation (ii) ,we obtain
→ 4×33 + y = 182
→ 132 +y = 182
→ y = 182-132
→ y = 50°
Therefore, y = 50°
Now,
→ ∠A = (2x-1) = (2×33-1) = 66-1 = 65°
→ ∠B = (y+5) = 50+5 = 55°
→ ∠C = (2y +15) =(2×50 +15) = 100+15 = 115°
→ ∠D = (4x -7) = (4×33 -7) = 132 -7 = 125°
Therefore ∠A = 65° , ∠B = 55° , ∠C = 115° and ∠D = 125°
since ABCD is a cyclic quadrilateral
angle A+angle C=180
therefore we get (x+y)=83
sum of all angles = 360
therefore we get (2x+y) = 116
thus
x=33 , y=50
angle D= 127