Question

find each measure. see example 3

1. m∠1
2. x
3. solve for x and state the angle relationship.
4. solve for x and state the angle relationship.
5. find the value of a and the measure of angle yzw.

Explanation:

21.

Step1: Identify angle - pair relationship

The angle with measure \(123^{\circ}\) and \(\angle1\) are vertical angles. Vertical angles are congruent.

Step2: Determine \(m\angle1\)

Since vertical angles are equal, \(m\angle1 = 123^{\circ}\)

Step1: Set up an equation

The angle with measure \(123^{\circ}\) and the angle \((3x + 6)^{\circ}\) are vertical angles. So, \(3x+6 = 123\).

Step2: Solve the equation for \(x\)

Subtract 6 from both sides: \(3x=123 - 6=117\). Then divide both sides by 3: \(x=\frac{117}{3}=39\).

Step1: Identify angle - pair relationship

The angles \(- 5+10x\) and \(9x + 1\) are corresponding angles. Corresponding angles are congruent when the lines are parallel. So, \(-5 + 10x=9x + 1\).

Step2: Solve the equation for \(x\)

Subtract \(9x\) from both sides: \(-5+10x-9x=9x + 1-9x\), which gives \(x-5 = 1\). Then add 5 to both sides: \(x=1 + 5=6\).

Answer:

\(m\angle1=123^{\circ}\)

22.