Read the proof. given: m∠h = 30°, m∠j = 50°, m∠p = 50°, m∠n = 100° prove: △hkj ~ △lnp statement reason 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∠n 6. substitution 7. ∠j ≅ ∠p; ∠k ≅ ∠n 7. if angles are equal then they are congruent 8. △hkj ~ △lnp 8. aa similarity theorem which reason is missing in step 2? cpctc definition of supplementary angles triangle parts relationship theorem triangle angle sum theorem

Step-by-step explanation:

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

To prove: △HKJ ~ △LNP

Proof:

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

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

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

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

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

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

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

Step 8. △HKJ ~ △LNP( AA similarity theorem)

Hence proved.

Thus, the missing step in 2 is (Triangle angle sum theorem)

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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