Question

3.2 practice with ca
in exercises 1 - 4, find (mangle1) and (mangle2).
1.
3.
in exercises 5 - 10, find the value of (x).
5.

Explanation:

Step1: Use corresponding - angles property

Corresponding angles are equal when two parallel lines are cut by a transversal.

Step2: Find \(m\angle1\) for Exercise 1

Since the angle of \(117^{\circ}\) and \(\angle1\) are corresponding angles, \(m\angle1 = 117^{\circ}\).

Step3: Use linear - pair property

\(\angle1\) and \(\angle2\) form a linear - pair. The sum of angles in a linear - pair is \(180^{\circ}\).

Step4: Calculate \(m\angle2\) for Exercise 1

\(m\angle2=180^{\circ}-m\angle1 = 180 - 117=63^{\circ}\).

Step5: Find \(m\angle1\) for Exercise 3

The angle of \(122^{\circ}\) and \(\angle1\) are corresponding angles, so \(m\angle1 = 122^{\circ}\).

Step6: Calculate \(m\angle2\) for Exercise 3

\(\angle1\) and \(\angle2\) form a linear - pair. So \(m\angle2 = 180^{\circ}-m\angle1=180 - 122 = 58^{\circ}\).

Step7: Find \(x\) for Exercise 5

The angle of \(128^{\circ}\) and \(2x^{\circ}\) are corresponding angles. So \(2x=128\).

Step8: Solve for \(x\)

Divide both sides of the equation \(2x = 128\) by 2. \(x=\frac{128}{2}=64\).

Answer:

Exercise 1: \(m\angle1 = 117^{\circ}\), \(m\angle2 = 63^{\circ}\)
Exercise 3: \(m\angle1 = 122^{\circ}\), \(m\angle2 = 58^{\circ}\)
Exercise 5: \(x = 64\)