### On Time

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

### Estimating Angles

How good are you at estimating angles?

### LOGO Challenge 8 - Rhombi

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

# Sharp Corners

##### Stage: 3 Challenge Level:

$140^{\circ}$.

Triangles have three angles, and the smallest angle is $20^{\circ}$. So the second smallest angle can be at least $20^{\circ}$ which leaves at most $180^{\circ}-(20^{\circ}+20^{\circ})=140^{\circ}$ for the largest angle (since the internal angles of a triangle sum to $180^{\circ}$).

This problem is taken from the UKMT Mathematical Challenges.

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