Question

lesson 2 angles and triangles
in the figure, ( mangle2 = 70^{circ} ). find the measure of each angle, then explain your reasoning by classifying the pair of angles.

1. ( angle7 )
2. ( angle5 )
3. ( angle15 )
4. ( angle10 )
5. ( angle14 )
6. ( angle11 )

Explanation:

Step1: Find \(m\angle7\)

\(\angle2\) and \(\angle7\) are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So \(m\angle7 = m\angle2=70^{\circ}\)

Step2: Find \(m\angle5\)

\(\angle2\) and \(\angle5\) are vertical angles. Vertical angles are equal. So \(m\angle5 = m\angle2 = 70^{\circ}\)

Step3: Find \(m\angle15\)

\(\angle2\) and \(\angle15\) are alternate - exterior angles. Alternate - exterior angles are equal when two parallel lines are cut by a transversal. So \(m\angle15=m\angle2 = 70^{\circ}\)

Step4: Find \(m\angle10\)

\(\angle2\) and \(\angle10\) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So \(m\angle10=m\angle2=70^{\circ}\)

Step5: Find \(m\angle14\)

\(\angle10\) and \(\angle14\) are vertical angles. Vertical angles are equal. Since \(m\angle10 = 70^{\circ}\), then \(m\angle14=m\angle10 = 70^{\circ}\)

Step6: Find \(m\angle11\)

\(\angle10\) and \(\angle11\) are supplementary angles (they form a linear pair). So \(m\angle11=180^{\circ}-m\angle10\). Substitute \(m\angle10 = 70^{\circ}\), then \(m\angle11=180 - 70=110^{\circ}\)

Answer:

1. \(m\angle7 = 70^{\circ}\) (corresponding angles)
2. \(m\angle5 = 70^{\circ}\) (vertical angles)
3. \(m\angle15 = 70^{\circ}\) (alternate - exterior angles)
4. \(m\angle10 = 70^{\circ}\) (alternate - interior angles)
5. \(m\angle14 = 70^{\circ}\) (vertical angles)
6. \(m\angle11 = 110^{\circ}\) (supplementary angles)