x = 7° and y = 4°
Solution:
Given JKLM is a cyclic quadrilateral.
∠J = 99°, ∠K = 7x°, ∠L = (11x + y)° and ∠M = 131°
In cyclic quadrilateral, sum of the opposite angles equal to 180°.
m∠K + m∠M = 180°
7x° + 131° = 180°
Subtract 131° from both sides of the equation.
7x° = 49°
Divide by 7 on both sides of the equation.
x = 7°
In cyclic quadrilateral, sum of the opposite angles equal to 180°.
m∠J + m∠L = 180°
99° + (11x + y)° = 180°
99° + 11(7°) + y° = 180°
176° + y° = 180°
Subtract 176° from both sides of the equation.
y = 4°
Hence x = 7° and y = 4°.
