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Right Time

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?

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Isosceles

Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.

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Linkage

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

Descending Angles

Age 11 to 14 Short Challenge Level:

Since the three angles in each triangle must add up to 180 degrees, 115 cannot be in the same triangle as 85 or 75, so 85 and 75 must be in the same triangle. 75+85=160 so the remaining angle in this triangle is 180 - 160 = 20 degrees.

This leaves the other two angles in the list together (115 and 35) which sum to give 150, so the other angle not included in the list is 180 - 150 = 30 degrees.

Therefore the complete list is 115, 85, 75, 35, 30, 20, so the smallest angle is 20 degrees.
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