MG2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms. California Standards

Vocabulary vertical angles adjacent angles complementary angles supplementary angles

Angles are congruent if they have the same measure. Adjacent angles are two angles that are side by side and have a common vertex and ray. Adjacent angles may or may not be congruent. MRN and NRQ are adjacent angles. They share vertex R and RN. NRQ and QRP are adjacent angles. They share vertex R and RQ.

Vertical angles are two angles that are formed by two intersecting lines and are not adjacent. Vertical angles have the same measure, so they are always congruent. MRP and NRQ are vertical angles. MRN and PRQ are vertical angles.

Additional Example 1: Identifying Adjacent and Vertical Angles Tell whether the numbered angles are adjacent or vertical. A. 5 6 5 and 6 are opposite each other and are formed by two intersecting lines. They are vertical angles.

Additional Example 1: Identifying Adjacent and Vertical Angles Tell whether the numbered angles are adjacent or vertical. B. 7 and 8 are side by side and have a common vertex and ray. 7 8 They are adjacent angles.

Tell whether the numbered angles are adjacent or vertical. Check It Out! Example 1 Tell whether the numbered angles are adjacent or vertical. A. 3 and 4 are side by side and have a common vertex and ray. 3 4 They are adjacent angles.

Tell whether the numbered angles are adjacent or vertical. Check It Out! Example 1 Tell whether the numbered angles are adjacent or vertical. B. 7 8 7 and 8 are opposite each other and are formed by two intersecting lines. They are vertical angles.

Complementary angles are two angles whose measures have a sum of 90°. 65° + 25° = 90° LMN and NMP are complementary. P N M L 25° 65°

Supplementary angles are two angles whose measures have a sum of 180°. 65° + 115° = 180° GFE and HJK are supplementary. K E F 115° 65° G H J

Additional Example 2: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. A. OMP and PMQ To find mPMQ, start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° – 75° = 30°. mOMP = 75° – 15° = 60°. O N P Q R M Since 60° + 30° = 90°, PMQ and OMP are complementary.

If the angle you are measuring appears obtuse, then its measure is greater than 90°. If the angle you are measuring is acute, its measure is less than 90°. Reading Math

Additional Example 2: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. B. NMO and OMR mNMO = 15° and mOMR = 165° O N P Q R M Since 15° + 165° = 180°, NMO and OMR are supplementary.

Additional Example 2: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. C. PMQ and QMR To find mPMQ, start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° – 75° = 30°. mQMR = 75°. O N P Q R M Since 30° + 75° = 105°, PMQ and QMR are neither complementary nor supplementary.

Check It Out! Example 2 Use the diagram to tell whether the angles are complementary, supplementary, or neither. A. BAC and CAF mBAC = 35° and mCAF = 145° Since 35° + 145° = 180°, BAC and CAF are supplementary. C B D E F A

Check It Out! Example 2 Use the diagram to tell whether the angles are complementary, supplementary, or neither. B. CAD and EAF To find mCAD, start with the measure that DA crosses, 90°, and subtract the measure that CA crosses, 35°. mCAD = 90° – 35° = 55°. mEAF = 35°. D Since 55° + 35° = 90°, CAD and EAF are complementary. E C B F A

Check It Out! Example 2 Use the diagram to tell whether the angles are complementary, supplementary, or neither. C. BAC and EAF mBAC = 35° and mEAF = 35° Since 35° + 35° = 70°, BAC and EAF are neither supplementary nor complementary. C B D E F A