Four-sided Figures: Finding Unknown Angles - Part 3
1. Find the unknown marked angle in the figure below.
Δ ABD is an isosceles triangle.
Therefore,
∠ADB = ∠ABD
And,
∠DAB + ∠ADB + ∠ABD = 180°
∠DAB = 180° − 46° = 88°
∠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°
∠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°
∠k = 92° − ∠ADB = 92° − 46° = 46°