Consider this right triangle with given measures.

9 cm

Step-by-step explanation:

We can use the Pythagorean theorem

a^2+b^2 = c^2

12^2+b^2 = 15^2

144 +b^2 = 225

Subtract 144 from each side

144-144+b^2 = 225-144

b^2 = 81

Take the square root of each side

sqrt(b^2) = sqrt(81)

b = 9

nlgqer

step-by-step

m∠5 + m∠3 = m∠1   is true.

m∠5 + m∠6 = 180 is true

m∠2 +m∠3 = m∠6   is true

m∠2 +m∠3 +m∠5 = 180   is true