DAY 49

Comment

Imagine that points A, B and C are fixed but that D moves further and further to the right.
What happens to the direction of line AD and to the size of angle A ?

Answer

The size of angle A can be up to (but not including) 140°.

Readers' methods

Kirsty J, Rickmansworth WD3:
Angle D can be as close as you like to 0°,
so the Maximum value of angle A is given by
Max + 80 + Max + 0 = 360
(because the angles add up to 360° and angle A = angle C ).
So Max = 140
(check: 140 + 80 + 140 + 0 = 360).

Paul N, Wimbledon SW19:
Since ABC is an isosceles triangle, angle BAC = angle BCA = 50 degrees.
To maximise angle CAD and thus angle BAD, the distance BD is extended towards infinity.
As BD approaches infinity, angle CAD approaches a right angle.
Therefore angle BAD will approach 50 + 90 = 140 degrees.