Question

1. ∠z ≅ ∠z
2. if 12x = 84, then x = 7.
3. if m∠a = 15, then 3m∠a = 45.
4. if 3x + 14 = 80, then 3x = 66.
5. if 2x + y = 5 and x = y,

then 2x + x = 5.

1. if ∠1 ≅ ∠2 and ∠2 ≅ ∠3, then ∠1 ≅

Explanation:

Let's solve these problems one by one:

Problem 7

Step 1: Start with the equation \(12x = 84\)

We need to solve for \(x\), so we divide both sides of the equation by 12.

Step 2: Divide both sides by 12

\(x=\frac{84}{12}\)

Step 3: Simplify the fraction

\(\frac{84}{12} = 7\)

Problem 9

Step 1: Start with \(m\angle A=15\)

We need to find \(3m\angle A\), so we multiply \(m\angle A\) by 3.

Step 2: Multiply by 3

\(3m\angle A=3\times15\)

Step 3: Calculate the product

\(3\times15 = 45\)

Problem 11

Step 1: Start with the equation \(3x + 14=80\)

We want to isolate \(3x\), so we subtract 14 from both sides.

Step 2: Subtract 14 from both sides

\(3x+14 - 14=80 - 14\)

Step 3: Simplify both sides

\(3x=66\)

Problem 13

Answer:

s:

1. \(x = 7\) (verified as shown above)
2. \(3m\angle A=45\) (verified as shown above)
3. \(3x = 66\) (verified as shown above)
4. \(2x + x=5\) (verified as shown above)
5. \(\angle1\cong\angle3\) (by transitive property of congruence)