30 Questions
Can two obtuse angles form a linear pair?
No
Which pair of angles below form a linear pair?
65° and 90°
What type of angles are ∠1 and ∠3 in relation to each other?
Vertically opposite angles
If ∠1 is 70 degrees, what is the measure of ∠3?
70 degrees
When two lines intersect, what kind of angles are ∠1 and ∠2?
Vertically opposite angles
What happens when you rotate a copy of the figure by 180 degrees after fixing it at the point of intersection?
The lines overlap perfectly on top of each other.
Which of the following pairs of angles are vertically opposite angles?
(∠COB, ∠AOD)
What is the complement of a 40º angle?
60º
In the figure, if ∠1 and ∠2 are supplementary and ∠1 is decreased, what should happen to ∠2 for them to remain supplementary?
Increase
Can two obtuse angles be supplementary?
Yes
If an angle is greater than 45º, what can be said about its complementary angle?
Less than 45º
In the figure, which pair of angles forms a linear pair?
(∠COB, ∠BOD)
If two angles are complementary, what is the sum of their measures?
90 degrees
What do two angles form if their sum is 180 degrees?
Linear pair
In a linear pair of angles, what is the total measure of the two angles?
180 degrees
What do two adjacent supplementary angles form?
Linear pair
In a figure where two lines intersect at a point, what are vertically opposite angles?
Equal
If one pair of vertically opposite angles at an intersection point are acute, what are the other pair?
Obtuse
In the context of parallel lines and transversals, what do alternate interior angles have in common?
They lie between the two lines
What distinguishes corresponding angles from other angle pairs?
They are in 'corresponding' positions relative to the two lines
Which type of angle pairs have the property of having different vertices and being in 'corresponding' positions?
Pairs of corresponding angles
What is a key characteristic of exterior angles formed by a transversal with parallel lines?
They add up to 180 degrees
Which statement best describes pairs of alternate exterior angles?
They are on opposite sides of the transversal and have different vertices
When drawing a transversal to parallel lines, what should be true about the alternate interior angles created?
They should have different vertices
What do we call angles that have a common vertex and a common arm but no common interior?
Adjacent angles
What type of angles are equal in measure when two lines intersect?
Vertical angles
What relationship is observed between the angles ∠1 and ∠5 when a transversal cuts two parallel lines?
They are corresponding angles
What type of angles are ∠3 and ∠6 in relation to each other?
Alternate interior angles
What do we call the meeting point of two lines when they intersect?
Intersection point
Which type of angles are ∠4 and ∠5 in relation to each other when two lines intersect?
Vertical angles
Study Notes
Angle Relationships
- Two obtuse angles cannot form a linear pair.
- When two lines intersect, they form a linear pair, and the angles are supplementary.
Linear Pairs
- ∠1 and ∠2 form a linear pair, and their sum is 180 degrees.
- If ∠1 is 70 degrees, then ∠3 is 110 degrees.
Vertically Opposite Angles
- ∠1 and ∠3 are vertically opposite angles.
- When two lines intersect, vertically opposite angles are equal in measure.
Complementary Angles
- The complement of a 40º angle is 50º.
- If an angle is greater than 45º, its complementary angle is less than 45º.
Supplementary Angles
- If two angles are supplementary, their sum is 180 degrees.
- If two angles are complementary, their sum is 90 degrees.
- If ∠1 and ∠2 are supplementary and ∠1 is decreased, ∠2 must increase to remain supplementary.
Parallel Lines and Transversals
- Alternate interior angles have the same measure.
- Corresponding angles have the same measure and are in the same relative position.
- Exterior angles formed by a transversal with parallel lines are supplementary.
- Alternate exterior angles have the same measure.
- When drawing a transversal to parallel lines, alternate interior angles are equal in measure.
Angle Types
- Adjacent supplementary angles form a linear pair.
- Vertically opposite angles are equal in measure.
- Corresponding angles are equal in measure.
- Alternate interior angles are equal in measure.
- Alternate exterior angles are equal in measure.
General Angle Facts
- When two lines intersect, the vertically opposite angles are equal in measure.
- The meeting point of two lines when they intersect is called the point of intersection.
Test your knowledge on angles with questions about adjacency of angles, finding angle values, filling in blanks about complementary and supplementary angles, and relationships between angles formed by lines intersecting.
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