Understanding Complementary and Supplementary Angles

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Questions and Answers

What is the complement of a 35 degree angle?

55 degrees

Two angles are called ______ if their sum is 90 degrees.

complementary

Which pair of angles are supplementary?

110 degrees and 70 degrees

130 degrees and 50 degrees (correct)

45 degrees and 45 degrees

20 degrees and 70 degrees

The supplement of a 120 degree angle is 60 degrees.

False Signup and view all the answers

Match each angle with its correct definition.

Acute = An angle less than 90 degrees Right = An angle equal to 90 degrees Obtuse = An angle greater than 90 degrees and less than 180 degrees Straight = An angle equal to 180 degrees Signup and view all the answers

If two angles are supplementary and one angle is decreased, what happens to the other angle?

The other angle increases by the same amount. Signup and view all the answers

Can two obtuse angles be supplementary?

No Signup and view all the answers

A 90 degree angle is its own complement.

True Signup and view all the answers

What is the complementary angle of an angle greater than 45°?

Less than 45° Signup and view all the answers

Vertical opposite angles are always equal.

True Signup and view all the answers

What are adjacent angles?

Angles that share a common vertex and a common arm, but do not overlap. Signup and view all the answers

If two angles are supplementary, then the sum of their measures is ______.

180° Signup and view all the answers

Match the following angles with their properties:

Complementary = Sum of 90° Supplementary = Sum of 180° Adjacent = Next to each other Vertically Opposite = Equal angles when two lines intersect Signup and view all the answers

Two angles forming a linear pair are always complementary.

False Signup and view all the answers

What is the relationship between vertically opposite angles?

They are equal in measure. Signup and view all the answers

If two lines intersect at a point, then the vertically opposite angles are always ______.

equal Signup and view all the answers

Identify the pair of angles that do not form a linear pair.

∠AOB and ∠AOE Signup and view all the answers

Study Notes

Complementary Angles

Complementary angles add up to 90°.
Example: 20° and 70° (90° - 20° = 70°)

Supplementary Angles

Supplementary angles add up to 180°.
Example: 105° and 75° (180° - 105° = 75°)

Identifying Complementary and Supplementary Pairs

Determine if pairs of angles are complementary (sum is 90°) or supplementary (sum is 180°).

Angles Equal to Their Complements/Supplements

An angle equal to its complement is 45°.
An angle equal to its supplement is 90°.

Supplementary Angles and Decreasing One Angle

If one supplementary angle decreases, the other must increase by the same amount to maintain the sum of 180°.

Types of Angles in Supplementary Pairs

Two acute angles cannot be supplementary.
Two obtuse angles cannot be supplementary.
Two right angles are supplementary.

Complementary Angles and Values

If an angle is greater than 45°, its complement is less than 45°.

Adjacent and Vertically Opposite Angles

Adjacent angles share a common vertex and side.
Vertically opposite angles are formed by intersecting lines.
Linear pairs are adjacent and form a straight line (180°).

Identifying Angle Pairs

Use the given diagrams to identify pairs of angles (adjacent, vertically opposite, complementary, supplementary, linear pairs).

Identifying Properties of Angles

Analyze figures and identify various relationships between angles.

Angle Values in Figures

Use principles (e.g., vertically opposite angles are equal, adjacent angles on a straight line add up to 180°) to find unknown angles.

Summary of Terms

Complementary - Angles that add up to 90°.
Supplementary – Angles that add up to 180°.
Adjacent angles - Angles that share a common vertex and side.
Vertically opposite angles - Angles opposite each other when two lines intersect.
Linear pair - Two adjacent angles that form a straight line (180°).

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Description

Test your knowledge on complementary and supplementary angles with this quiz. Explore the definitions, examples, and properties of angles that add up to 90° and 180°. Challenge yourself to identify various pairs and properties related to these angle types.