Adjacent Angles
Non-overlapping adjacent angles are two angles that are right next to one another that share a ray/line segment but do not overlap. In the example (right) ∠ABC (20)° is adjacent to ∠CBD (40°). These two angles share a vertex ∠B and ray/line segment C. It is important for students to understand that these two angle form a new angle ∠ABD that measures 60°. The measure of the combined angles will become useful when your students are given only one of the measures for the two adjacent angles, the measurement of the two angles combined, and they must solve to determine the measurement of the remaining unknown angle. |
4.7E Determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures
Complementary Angles
Adjacent angles that are complementary (sum of 90˚) have a relationship that can be easily identified for students. You will notice that students will begin to use the 90° as a benchmark of the acute or obtuse nature of other angles. The angles in a set of complementary angles must sum to 90°, any less or more and the angles will remain adjacent but are not able to be classified as complementary in relationship. Examples:
It is very likely that your students will be asked to determine that ∠A equals 30° when given that ∠B measures 60° in a situation (Process TEKS) where the two angles are complementary. |
Supplementary Angles
Adjacent angles that are supplementary (sum of 180˚) have a relationship that can be easily identified for students. Here again, the right angle will become a touchstone as they grow in their visualization of obtuse, and acute angles and their relationship as supplementary. Supplementary angles do not have to be adjacent, but you should be able to rearrange the angles, place them adjacent to each other and form a straight angle (180°). Examples:
It is very likely that your students will be asked to determine that ∠A equals 50° when given that ∠B measures 130° in a situation (Process TEKS) where the two angles are supplementary. |