Question

given
ray yw bisects ∠xyz
m∠xyw = 9x + 9
m∠wyz = 100 - 4x
prove
m∠xyw = 72°
statement

1. ray yw bisects ∠xyz
2. m∠xyw = m∠wyz
3. m∠xyw = 9x + 9
4. m∠wyz = 100 - 4x
5. 9x + 9 = 100 - 4x
6. 9x = 91 - 4x
7. 13x = 91
8. x = 7
9. m∠xyw = 9(7) + 9
10. m∠xyw = 72°

reason

1. given
2. definition of angle bisector
3. given
4. given
5. substitution
6. subtraction property of equality
7. ?
8. division property of equality
9. substitution
10. algebra

Explanation:

Step1: Analyze the equation

We have the equation \(9x = 91-4x\). To get \(13x = 91\), we need to add \(4x\) to both sides of the equation.

Step2: Apply the property

The property used when we add \(4x\) to both sides of the equation \(a=b\) (here \(a = 9x\) and \(b=91 - 4x\)) is the Addition Property of Equality. The Addition Property of Equality states that if \(a=b\), then \(a + c=b + c\). In our case, \(c = 4x\), so \(9x+4x=(91 - 4x)+4x\), which simplifies to \(13x = 91\).

Answer:

Addition Property of Equality