Let's begin with recalling the Exterior Angle Inequality Theorem. This theorem tells us that the measure of an exterior angle of a triangle is greater than the measure of either of its corresponding remote interior angles.
Now, let's look at the given picture. As we can see, ∠5 is an exterior angle of a triangle containing ∠2 and ∠10. Therefore, the measures of angles 2 and 10 are less than the measure of ∠5.
Notice that, since ∠10 is an exterior angle of a triangle containing ∠7 and ∠8, the measures of ∠7 and ∠8 are less than m∠10. This indicates that m∠7 and m∠8 are also less than m∠5.
m ∠5 &> m ∠2
m ∠5 &> m ∠10 > m ∠7
m ∠5&> m ∠10 >m ∠8
Therefore, there are four angles, 2,7,8 and 10, that measure less than ∠5.
