Angle Theorems & Definitions (Review)

Angle Theorems & Definitions (Review)

Supplementary = 180° • Complementary = 90°

Vertical Angles Theorem • Vertical angles are equal in measure

Linear Pair • A pair of adjacent angles that are supplementary

Ex 1)

Ex 2) Write out equations for congruent relations & supplementary relationships

Triangle Sum Theorem • The sum of the angles in a triangle will always equal 180° x°+ y°+ z°= 180˚ x° y° z°

Base Angle Theorem Pt. 1 • Base angles in an isosceles triangle are always congruent X° X° x° = x°

Base Angle Theorem Pt.2 • If the base angles are congruent, then the sides are congruent X X x cm = xcm

Equilateral Triangles • All sides are congruent • All angles = 60°

Ex 3) m∠L = ____________ J 42° K 35° L

Ex 4) Find the measures of the two missing angles 80°

Ex 5) Find the measure of each angle

#1 m∠BAE = 50°, m∠DAC=_____ 50˚ 50˚ 50˚

#2 m∠BAE = 70°, m∠DAB=_____ 110˚ 110˚ 70˚

#3 m∠DAB = 6x+24m∠EAC = 5x – 49 SOLVE FOR X 6x + 24 5x + 49 X = 25

#4 m∠DAB = 4x+5m∠DAC = 2x + 1 SOLVE FOR X 4x + 5 2x + 1 X = 29

#5 m∠MNL = 50˚ m∠INJ= __________ 50˚ 50˚ 50˚

#6 m∠MNL = 60˚ m∠JNK= __________ 30˚ 60˚ 30˚

#7 m∠INM = 3x+5 m∠MNL=x+15Find the measure of each angle X = 40 125˚ 55˚ 55˚ 90˚ 35˚

#8 m∠JNI = 3x+5 m∠JNK=x+15Solve for x x = 17.5 3x+5 x+15

m∠A = 70˚ m∠C = 50˚ m∠B = _____ 70˚ 60˚ 50˚

m∠A = 80˚ m∠B = 20˚ m∠C = _____ 80˚ 20˚ 80˚

Solve for x X = 9 20x = 180 7x + 1 7x – 2 6x + 1

m∠7 = 50˚ m∠3 = 70˚ Find all other angle measures 50˚ 120˚ 60˚ 70˚ 110˚ 60˚ 120˚

m∠2 = 55˚ m∠7 = 80˚ Find all other angle measures 80˚ 125˚ 55˚ 45˚ 135˚ 55˚ 125˚

m∠3 = 65˚ Find all other angle measures 50˚ 115˚ 65˚ 65˚ 115˚ 65˚ 115˚

Angle Theorems & Definitions (Review)