Four-sided Figures: Finding Unknown Angles - Part 3

1. Find the unknown marked angle in the figure below.

geometry finding unknown angles in a 4-sided figure

Δ ABD is an isosceles triangle.
Therefore,
∠ADB  =  ∠ABD
And,
∠DAB  +  ∠ADB  +  ∠ABD  =  180°
∠DAB  =  180°  −  46°  =  88°
The angle sum of a triangle is 180°.
Now, since AB // DC,
∠DAB  +  ∠ADC  =  180°
∠ADC  =  180°  −  88°  =  92°
The sum of a pair of angles between two parallel lines is 180°.
Therefore,
∠k  =  92°  −  ∠ADB  =  92°  −  46°  =  46°