Geometry ! 1. fill in the blanks in the proof. don’t forget the missing angle in

Solution:

1)

Statement                                                     Reason

x  ║t                                                             Given

m∠16=m∠7                                                  Given

m∠16=m∠1                                                   Corresponding angles

m∠7=m∠1                                                      Substitution

k║w                                                               Alternate exterior angles equal

                                                                    (Property of parallel lines)

2)Part A:

Sum of angles in any triangle is 180 degrees.

m∠BAC+m∠ABC+m∠BCA= 180

Substituting the values :

4x+10+12x-6+3x+5=180

Adding like terms :

19x+9=180

19x=171

x=9.

Part B:

Substituting x value :

m∠BAC=4x+10=4(9)+10=46

m∠ABC=12x-6=12(9)-6=102

m∠BCA=3x+5=3(9)+5=32.

Part C:

m∠1=180-46=134

m∠2=180-102=78.

m∠3=180-32=148.

Part D:

Angle BAC and angle FAC are angle made on straight line and are linear .Such angles are called linear pairs.

Part E:

Angle BCE and Angle DCA are vertically opposite angles.

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