Four-sided Figures: Finding Unknown Angles - Part 3

Example:

Find the unknown marked angle in the figure below.


ΔABD is an isosceles triangle.
Therefore,
∠ADB = ∠ABD

The angle sum of a triangle is 180°.
And,
∠DAB + ∠ADB + ∠ABD = 180°
∠DAB = 180° - 46° - 46° = 88°

The sum of a pair of angles between two parallel lines is 180°.
Now, since AB // DC,
∠DAB + ∠ADC = 180°
∠ADC = 180° - 88° = 92°

Therefore,
∠k = 92° - ∠ADB = 92° - 46° = 46°