In the figure, \(l\parallel m\). Find \((b-a)\).
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 61°
Two facts settle the angles: a line crossing two parallel lines makes equal alternate angles with them, and an exterior angle of a triangle equals the sum of the two interior angles opposite it. The points are lettered in the figure below.
EA crosses the parallel lines l and m, so angle a (at E, between EA and l) and the 39° at A (between EA and m) are alternate angles: a = 39°
In triangle EDC, the 139° at D lies outside the triangle, between DC and l beyond D, so it is the exterior angle at D: \(a+b=139\)°
\(b=139-39=100\)°
\(b-a=100-39=61\)°