An important question from linear equations in two variables as it was already asked in various examinations in which we have been asked to find the angles of a cyclic quadrilateral ABCD if it is given that in a cyclic quadrilateral ABCD, ∠A=(2x+4),∠B=(y+3),∠C=(2y+10),∠D=(4x−5).
Kindly solve the above problem by using the properties of linear equations in two variables
RS Aggarwal, Class 10, chapter 3E, question no 53
Let ABCD be a cyclic quadrilateral.
∠A=2x+4,∠B=y+3,∠C=2y+10,∠D=4x−5
In cyclic quadrilateral the sum of the opposite angles in 180°. Therefore,
∠A+∠C=180°
⇒2x+4+2y+10=180°
⇒2x+2y=166°
⇒x+y=83°→1
∠B+∠D=180°
⇒y+3+4x−5=180°
⇒4x+y=182°→2
Solving 1 and 2, we get
4x+y−x−y=182°−83°
⇒3x=99°
⇒x=33°
& 33°+y=83°
⇒y=83°−33°
=50°
∴∠A=2×33°+4=70°,
∠B=50°+3=53°
∠C=2×50°+10=110°,
∠D=4×33°−5=127°