Answer:
Θ = 46°
Step-by-step explanation:
the angle between a tangent and a radius at the point of contact is 90° , so
∠ ABO = 90°
since OB = OD ( radii of circle ) then Δ BOD is isosceles and
∠ OBD = ∠ ODB = 22°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ AOB is an exterior angle of the triangle , then
∠ AOB = 22° + 22° = 44°
the sum of the 3 angles in Δ AOB = 180° , then
Θ + 44° + 90° = 180°
Θ + 134° = 180° ( subtract 134° from both sides )
Θ = 46°
y = ( 3 * x ) - 2.
This is because the card costs for 3 $ and should be multiplied by the number of total cards she buys in that particular day. So 3 * x.
Now as she has got a 2$ off coupon, whatever the total is she gets 2 dollars off on that price. So we will subtract 2 at that time. FInally all this summed up would be equal to y.
