How many degrees is angle x?
A normal-level "Angle" problem.Any zigzag between parallel lines yields to one move: draw a parallel line through the bend. It works however many bends there are.
GivenLine ℓ and line m are parallel
Hints
- Angle x sits at the point where the line bends. Let's call it P and start there.
- Add one construction line: through P, parallel to ℓ and m. Angle x is now split into an upper and a lower part.
- When one line crosses two parallel lines, the alternate angles are equal. The new line is parallel to ℓ, so these two angles are the same size.
- So the 32° above moves down to the upper side of P, unchanged.
- Same below. The new line is parallel to m too, so those alternate angles are equal as well.
- So the 45° below moves up to the lower side of P, unchanged.
- Angle x is simply those two angles gathered at P, added together.
- Just add them. 32° + 45°
Answer 77°
More "Angle" problems
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