How many degrees is angle x?
A hard-level "Angle" problem.Every folding problem runs on two facts: overlapping angles are equal, and the strip's parallel edges give equal alternate angles. An isosceles triangle always falls out.
GivenA strip of constant width folded once. The crease meets the lower edge at 65°
Hints
- The folded-over part lies exactly on top of the original. So the two angles on either side of the crease QP are always equal.
- The crease meets the lower edge at 65°, so the folded copy of that angle is also 65°. That is the first one.
- Next use the fact that the strip's two edges ℓ and m are parallel — the strip has the same width everywhere.
- The crease crosses two parallel lines, and alternate angles are equal, so the 65° at Q reappears at P. That is the second one.
- Clear the rest and look only at triangle PQR. Both base angles are 65°, so it is an isosceles triangle. "Folding makes an isosceles triangle" is the stock phrase for this whole family of problems.
- The three angles of a triangle add to 180°, so angle x is 180 − 65 − 65.
Answer 50°
More "Angle" problems
- How big is angle x?
- What is A＋B＋C＋D＋E?
- How big is angle BIC?
- How many degrees is angle x?
- How many degrees is angle x?
- What is the angle at the centre of the sector?