How big is angle x?
A hard-level "Angle" problem.Repeat one move and the numbers line up. Do not try to leap to the answer — do it twice, spot the step size, and the rest follows.
Given4 rods of equal length are joined end to end. The angle at the far left is 20°.
Hints
- All the rods are the same length, so the first triangle is isosceles. If one angle is 20°, the one facing it is 20° too.
- Now use "an exterior angle equals the two opposite interior angles added". Two lots of 20° make the next angle 40° — it has grown by 20°.
- The very same move again. The next triangle is isosceles too, giving two 40° angles, and the exterior angle is 20 + 40 = 60° — up by another 20°.
- Line them up: 20° → 40° → 60°. Each step adds exactly 20°.
- Angle x is the 3th step, so 20 × 3 = 60°. However many rods there are, the same counting works.
Answer 60度
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