Read the proof. Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° Prove: △HKJ ~ △LNP Triangles H K J and L N P are shown. Triangle L N P is smaller and to the right of triangle H K J. StatementReason 1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°1. given 2. m∠H + m∠J + m∠K = 180°2. ? 3. 30° + 50° + m∠K = 180°3. substitution property 4. 80° + m∠K = 180°4. addition 5. m∠K = 100°5. subtraction property of equality 6. m∠J = m∠P; m∠K = m∠N6. substitution 7. ∠J ≅ ∠P; ∠K ≅ ∠N7. if angles are equal then they are congruent 8. △HKJ ~ △LNP8. AA similarity theorem Which reason is missing in step 2? CPCTC definition of supplementary angles triangle parts relationship theorem triangle angle sum theorem

The correct option is;

Triangle angle sum theorem

Step-by-step explanation:

Statement                                                                        Reason

1. m∠H = 30° m∠J = 50°, m∠P = 50° m∠N = 100°           Given

2. ∠H + m∠J + m∠K = 180°                                  (Triangle angle sum theorem)

3. 30° + 50° + m∠K = 180°                                                (Substitution property)

4. 80° + m∠K = 180°                                                          (addition)

5. m∠K = 100°                                                                    (subtraction property)

6. m∠J = m∠P; m∠K = m∠N                                              (substitution)

7. m∠J ≅ m∠P; m∠K ≅ m∠N If angles are equal then they are congruent

8. ΔHKJ ~ ΔLNP      AA similarity theorem.

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."