☰ Contents · Geometry

Angle types. Adjacent and vertical angles

Lessons 12–13 · 2 lessons · Geometry Grade 7, corrected and expanded 3rd edition. Yangiyo‘l Poligraf Servis, Tashkent, 2017 (approved by the Ministry of Public Education)
12

Types of angles: right, acute, obtuse. The bisector

Textbook: pp. 32–33
GoalClassify angles and work with the bisector.
New words
right angle · to‘g‘ri burchakacute angle · o‘tkir burchakobtuse angle · o‘tmas burchakbisector · bissektrisa
Explanation

By measure, angles are classified as acute (less than 90°), right (equal to 90°) and obtuse (between 90° and 180°). A straight angle equals 180°. The ray starting at the vertex that splits an angle into two equal angles is called the bisector of that angle. If ∠AOB = 80°, the bisector makes two angles of 40° each. Angles and their measures are often denoted by Greek letters α, β, γ. When solving, call the unknown angle x and write an equation using the addition property of angle measures.

Worked examples
Rays OB and OC divide ∠AOD = 120° into three equal angles α: 3α = 120°, α = 40° — all acute.
OC bisects ∠AOB = 70°: ∠AOC = ∠COB = 70° : 2 = 35°.
Class activity

“Name the type”: cards show 15°, 90°, 135°, 180°, 62°, 91°; pupils sort them into acute, right, obtuse and straight.

Practice
1
The bisector divides ∠AOB = 96° into two angles. Find each (degrees).
2
What type is a 118° angle?
3
∠AOD = 150° is divided into three equal angles. Each is how many degrees?
4
Why are the angles made by the bisector of an acute angle also acute?