Question

example 4
in the figure, ( mangle 7 = 100^circ ). find the measure of each angle.

1. ( angle 9 )
2. ( angle 6 )
3. ( angle 8 )
4. ( angle 2 )
5. ( angle 5 )
6. ( angle 11 )

Explanation:

To solve for the measures of the angles, we use properties of vertical angles, linear pairs, and parallel lines (assuming the lines are parallel as indicated by the arrows). Let's solve each angle one by one:

21. \( \angle 9 \)

• \( \angle 7 \) and \( \angle 9 \) are vertical angles. Vertical angles are equal.

\( m\angle 9 = m\angle 7 = 100^\circ \)

22. \( \angle 6 \)

• \( \angle 6 \) and \( \angle 7 \) form a linear pair (they are adjacent and supplementary).

\( m\angle 6 + m\angle 7 = 180^\circ \)
\( m\angle 6 = 180^\circ - 100^\circ = 80^\circ \)

23. \( \angle 8 \)

• \( \angle 8 \) and \( \angle 7 \) are vertical angles. Vertical angles are equal.

\( m\angle 8 = m\angle 7 = 100^\circ \)

24. \( \angle 2 \)

• \( \angle 2 \) and \( \angle 6 \) are corresponding angles (assuming the lines are parallel). Corresponding angles are equal.

\( m\angle 2 = m\angle 6 = 80^\circ \)

25. \( \angle 5 \)

• \( \angle 5 \) and \( \angle 9 \) are corresponding angles (assuming the lines are parallel). Corresponding angles are equal.

\( m\angle 5 = m\angle 9 = 100^\circ \)

26. \( \angle 11 \)

• \( \angle 11 \) and \( \angle 7 \) are corresponding angles (assuming the lines are parallel). Corresponding angles are equal.

\( m\angle 11 = m\angle 7 = 100^\circ \)

Final Answers:

1. \( \boldsymbol{100^\circ} \)
2. \( \boldsymbol{80^\circ} \)
3. \( \boldsymbol{100^\circ} \)
4. \( \boldsymbol{80^\circ} \)
5. \( \boldsymbol{100^\circ} \)
6. \( \boldsymbol{100^\circ} \)

Answer:

To solve for the measures of the angles, we use properties of vertical angles, linear pairs, and parallel lines (assuming the lines are parallel as indicated by the arrows). Let's solve each angle one by one:

21. \( \angle 9 \)

• \( \angle 7 \) and \( \angle 9 \) are vertical angles. Vertical angles are equal.

\( m\angle 9 = m\angle 7 = 100^\circ \)

22. \( \angle 6 \)

• \( \angle 6 \) and \( \angle 7 \) form a linear pair (they are adjacent and supplementary).

\( m\angle 6 + m\angle 7 = 180^\circ \)
\( m\angle 6 = 180^\circ - 100^\circ = 80^\circ \)

23. \( \angle 8 \)

• \( \angle 8 \) and \( \angle 7 \) are vertical angles. Vertical angles are equal.

\( m\angle 8 = m\angle 7 = 100^\circ \)

24. \( \angle 2 \)

• \( \angle 2 \) and \( \angle 6 \) are corresponding angles (assuming the lines are parallel). Corresponding angles are equal.

\( m\angle 2 = m\angle 6 = 80^\circ \)

25. \( \angle 5 \)

• \( \angle 5 \) and \( \angle 9 \) are corresponding angles (assuming the lines are parallel). Corresponding angles are equal.

\( m\angle 5 = m\angle 9 = 100^\circ \)

26. \( \angle 11 \)

• \( \angle 11 \) and \( \angle 7 \) are corresponding angles (assuming the lines are parallel). Corresponding angles are equal.

\( m\angle 11 = m\angle 7 = 100^\circ \)

Final Answers:

1. \( \boldsymbol{100^\circ} \)
2. \( \boldsymbol{80^\circ} \)
3. \( \boldsymbol{100^\circ} \)
4. \( \boldsymbol{80^\circ} \)
5. \( \boldsymbol{100^\circ} \)
6. \( \boldsymbol{100^\circ} \)