Geometry ! 1. fill in the blanks in the proof. don’t forget the missing angle in step 4 2. (part a) use the given information to find the value of x. (part b) now that you know x, find the measure of each angle. m (part c) find the measures of the additional angles in the picture above. m< 1 = m< 2= (part d) angle bac and angle fac are an example of what type of angles? (part e) angle bce and angle dca are an example of what type of angles?

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.

.

the distance between point a and point b is 6 units

1) is right

step-by-step explanation: