Question

In parallelogram ABCD, AP and AQ are perpendiculars from the vertex of obtuse angle A as shown.
If  ∠x: ∠y = 2 : 1.
find angles of the parallelogram.

Answer 1

We know that AQCP is a quadrilateral. So sum of all angles must be 360.
∴ x + y + 90 + 90 = 360
x + y = 180
Given x : y = 2 : 1
So substitute x = 2y
3y = 180
y = 60
x = 120

We know that angle C = angle A = x = 120
Angle D = Angle B = 180 − x = 180 − 120 = 60
Hence, angles of a parallelogram are 120, 60, 120 and 60.