If AB ∩ CD = Ø, in the same plane, then .......... If two straight lines parallel to a third, then they are .......... Find the value of x = .......... If two adjacent angles are c... If AB ∩ CD = Ø, in the same plane, then .......... If two straight lines parallel to a third, then they are .......... Find the value of x = .......... If two adjacent angles are complementary, then their outer sides are ..........
Understand the Problem
The question includes multiple mathematics problems dealing with geometry, specifically concerning lines, angles, and algebraic expressions related to a diagram. The questions ask about the relationships between lines and angles, requiring understanding of parallel lines and complementary angles.
Answer
5. Parallel lines 6. Parallel 7. $x = 35$ 8. Opposite rays
Answer for screen readers
- Parallel lines
- Parallel
- $x = 35$
- Opposite rays
Steps to Solve
- Understanding Intersection of Lines
The first question states that if lines ( AB ) and ( CD ) do not intersect (indicated by ( AB \cap CD = \emptyset )), they are parallel. Therefore, the answer is "parallel lines."
- Parallel Lines Implication
The second question states if two straight lines are parallel to a third line, then they are also parallel to each other. Thus, the answer is "parallel."
- Finding the Value of ( x )
Given the angle measures:
- One angle is ( 4x )
- The other angle is ( 40 )
Since they form a straight line, they sum up to ( 180^\circ ): $$ 4x + 40 = 180 $$
- Solving for ( x )
Subtract ( 40 ) from both sides: $$ 4x = 180 - 40 $$
This simplifies to: $$ 4x = 140 $$
Now divide by ( 4 ): $$ x = \frac{140}{4} $$
- Understanding Complementary Angles
The last question states that if two adjacent angles are complementary, then their outer sides are opposite rays. This is the definition of complementary angles.
- Parallel lines
- Parallel
- $x = 35$
- Opposite rays
More Information
- Complementary angles sum to ( 90^\circ ).
- The concept of parallel lines is crucial in geometry for understanding angles formed by transversals.
Tips
- Mistaking non-intersecting lines for being intersecting.
- Forgetting to correctly apply the sum of angles relationships when solving for ( x ).
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