Question

2 Questions, 100 Points. Show ALL WORK

Answer 1

1) vertical

• angles that lie opposite to each other by the intersection of two lines are called vertically opposite angles.
• vertical angles are congruent in nature .

2) complementary ; adjacent

• complementary angles add up to 90° .
• angles sharing a common vertex and common side are termed as adjacent angles.

Answer 2

Answer:

1) Vertical

2) Complementary

Step-by-step explanation:

Question 1

Vertical angles are a pair of non-adjacent angles formed by the intersection of two lines, sharing a common vertex.

The diagram shows two intersecting line segments. At their point of intersection, four angles are formed. One pair of vertically opposite angles is labeled 'a' and 'b'. Therefore, the relationship between angles 'a' and 'b' is:

$\LARGE\boxed{\boxed{\sf Vertical}}$

$\dotfill$

Question 2

Adjacent angles are angles that share a common side and vertex but do not overlap.

Complementary angles are two angles whose measures sum to 90°, regardless of their position or adjacency to each other.

The diagram shows two straight lines intersecting at right angles. A ray begins at the point of intersection, dividing one of the resulting quadrants into two adjacent angles labelled 'a' and 'b'. As the sum of these angles is 90°, then the relationship between angles 'a' and 'b' is:

$\LARGE\boxed{\boxed{\sf Complementary}}$

Note that we can also call these angles adjacent, since they share a common side and vertex. However, since diagram explicitly tells us that the sum of these angles is a right angle (90°), it is more accurate to refer to them as complementary angles.

$\dotfill$

Additional Information

• Complementary angles are two angles whose measures sum to 90°, regardless of their position or adjacency to each other.
• Supplementary angles are two angles whose measures sum to 180°, regardless of their position or adjacency to each other.
• Vertical angles are a pair of non-adjacent angles formed by the intersection of two lines, sharing a common vertex, and are always congruent.
• Adjacent angles are angles that share a common side and vertex but do not overlap.