1.4 Angles & their Measures

1.4 Angles & their Measures p. 26

Angle symbol: • 2 rays that share the same endpoint (or initial point) Sides – the rays XY & XZ Vertex – the common endpoint; X Y X 5 Z Named <YXZ, <ZXY (vertex is always in the middle), or <X (if it’s the only <X in the diagram). Angles can also be named by a #. (<5)

There are 3 different <B’s in this diagram; therefore, none of them should be called <B. A <B ? D B C

m<A means the “measure of <A” Measure angles with a protractor. Units of angle measurement are degrees (o). Angles with the same measure are congruent angles. If m<A = m<B, then <A <B. Angle Measurement

Postulate 3: Protractor Post. • The rays of an angle can be matched up with real #s (from 1 to 180) on a protractor so that the measure of the < equals the absolute value of the difference of the 2 #s. 55o 20o m<A = 55-20 = 35o

B is ___________ C is ___________ D is ___________ Interior or Exterior? in the interior in the exterior on the < B C D A

Post. 4: Angle Addition post. • If P is in the interior of <RST, then m<QRP + m<PRS = m<QRS. If m<QRP=5xo, m<PRS=2xo, & m<QRS=84o, find x. 5x+2x=84 7x=84 x=12 m<QRP=60o m<PRS=24o S P Q R

Acute angle – Right angle – Obtuse angle – Straight angle – Measures between 0o & 90o Measures exactly 90o Measures between 90o & 180o Measures exactly 180o Types of Angles

Adjacent Angles • 2 angles that share a common vertex & side, but have no common interior parts. (they have the same vertex, but don’t overlap) such as <1 & <2 2 1

Name an acute angle <3, <2, <SBT, or <TBC Name an obtuse angle <ABT Name a right angle <1, <ABS, or <SBC Name a straight angle <ABC Example: S T 3 1 2 A B C

Assignment

1.4 Angles & their Measures