Fill in the blanks. Complete the sentences. Illustrate if necessary. 1. Point B is between points A and C. If segment AC is 55 units and segment AB is 11 units, then segment BC is... Fill in the blanks. Complete the sentences. Illustrate if necessary. 1. Point B is between points A and C. If segment AC is 55 units and segment AB is 11 units, then segment BC is __ units. 2. Segment ML is 37 units long. If point N is the midpoint of segment ML, then segment MN is __ units. 3. If point E is the midpoint of segment DF and segment DE is 13 units long, then segment DF is __ units. 4. If angles W, X, Y, and Z are formed by two perpendicular lines, then each of them measures exactly __. 5. Angle M and angle V are complementary angles. If angle M measures 43 degrees, then the measure of angle V is __ degrees. 6. Angle J and angle H are supplementary angles. If angle J measures 95 degrees, then the measure of angle H is __ degrees. 7. Angle O and angle P are vertical angles. If angle O measures 122 degrees, then the measure of angle P is __ degrees. 8. Angle R and angle S form a linear pair. If angle R measures 107 degrees, then the measure of angle S is __ degrees. II. Find the measure of angle b. Show your solution.
Understand the Problem
The question is asking to find the measures of certain angles and segments based on given lengths and angle relationships, such as complementary and supplementary angles.
Answer
- Problem 9: \( b = 43^\circ \) - Problem 10: \( b = 47^\circ \) - Problem 11: \( b = 63^\circ \) - Problem 12: \( b = 50^\circ \)
Answer for screen readers
- Problem 9: ( b = 43^\circ )
- Problem 10: ( b = 47^\circ )
- Problem 11: ( b = 63^\circ )
- Problem 12: ( b = 50^\circ )
Steps to Solve
-
Finding angle ( b ) using vertical angles (Problem 9)
Vertical angles are equal. Since angle ( mLb ) is given as ( 43^\circ ), angle ( b ) must also be ( 43^\circ ). -
Finding angle ( b ) using complementary angles (Problem 10)
The problem states that the two angles form a linear pair. Therefore, we can write:
$$ mLb + b = 90^\circ $$
Substituting ( mLb = 43^\circ ):
$$ 43^\circ + b = 90^\circ $$
Solving for ( b ):
$$ b = 90^\circ - 43^\circ = 47^\circ $$ -
Finding angle ( b ) (Problem 11-12)
Given that ( mLb = 27^\circ ), we can again use the linear pair relationship:
$$ b + mLb = 90^\circ $$
Thus,
$$ b + 27^\circ = 90^\circ $$
Solving gives:
$$ b = 90^\circ - 27^\circ = 63^\circ $$ -
Finding angle ( b ) using supplementary angles (Problem 13-14)
For angle ( mLb = 130^\circ ):
$$ b + mLb = 180^\circ $$
Substituting and solving:
$$ b + 130^\circ = 180^\circ $$
$$ b = 180^\circ - 130^\circ = 50^\circ $$
- Problem 9: ( b = 43^\circ )
- Problem 10: ( b = 47^\circ )
- Problem 11: ( b = 63^\circ )
- Problem 12: ( b = 50^\circ )
More Information
In problems involving angle relationships, knowing whether angles are complementary, supplementary, or vertical helps in calculating unknown angles. Vertical angles are always equal, while complementary angles sum to ( 90^\circ ) and supplementary angles sum to ( 180^\circ ).
Tips
- Confusing complementary and supplementary angles can lead to incorrect calculations. Always remember:
- Complementary angles add up to ( 90^\circ )
- Supplementary angles add up to ( 180^\circ )
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