Sure! Let's go through each statement step-by-step.
1. Fill in the blanks for the given statements:
Sum to 90°:
- Two angles are complementary if the sum of their measures is 90°. In other words, if you have two angles that add up to 90°, they are called complementary angles.
Sum to 180°:
- Two angles are supplementary if the sum of their measures is 180°. This means that if you add the measures of two angles and get 180°, they are considered supplementary angles.
2. Complete each statement:
- Sum to 90°:
- Two angles are complementary if the sum of their measures is 90°.
- Sum to 180°:
- Two angles are supplementary if the sum of their measures is 180°.
3. The complement of a 30° angle has a measure of:
- To find the complement of a 30° angle, we subtract the angle from 90° (since complementary angles sum to 90°).
- The complement of a 30° angle is [tex]\(90° - 30°\)[/tex].
- So, the complement of a 30° angle is 60°.
4. The supplement of a 65° angle has a measure of:
- To find the supplement of a 65° angle, we subtract the angle from 180° (since supplementary angles sum to 180°).
- The supplement of a 65° angle is [tex]\(180° - 65°\)[/tex].
- So, the supplement of a 65° angle is 115°.
5. Opposite & Congruent:
- Vertical angles (created when two lines intersect) are opposite each other and are always congruent (they have the same measure).
So, in summary:
1. Sum to 90°:
- Two angles are complementary if the sum of their measures is 90°.
2. Sum to 180°:
- Two angles are supplementary if the sum of their measures is 180°.
3. The complement of a 30° angle has a measure of:
- 60°.
4. The supplement of a 65° angle has a measure of:
- 115°.
5. Opposite & Congruent:
- Vertical angles are opposite each other and are congruent.
