1 answer:
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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