Question

ONKA is a square with ∠KON = 45°. Determine ∠KOA.​

Answer 1

Given,

ONKA is a square.

∠KON = 45°

To find,

Find ∠KOA.

Solution,

We can solve this problem with the help of the figure below.

If ONKA is a square, all four angles of square ONKA are 90°.

∠KON = 45° is half of ∠NOA.

∠NOA must be 90° (Angle of a square)

∴ ∠KOA= ∠NOA-∠KON

            = 90°-45°

            = 45°

Or

In both angles(∠KON and ∠KOA), KO is common.

ON parallel AK

∴ ∠KON= ∠ OKA= 45°

∠ KAO= 90° (Angle of a square)

KOA becomes an isosceles triangle. (Sides of the square are equal)

∴ ∠KOA=45°

Thus, Angle KOA is equal to 45°.