Answer:
Blank 1 : 45
Blank 2 : 75
Blank 3 : 60
Blank 4 : 41
Blank 5 : 71
Blank 6 : 109
Explanation:
You got answers to questions 1 and 2 correct.
m∠1 = 45° because ∠1 is vertically opposite to the angle measuring 45°
m∠2 = 75° for the same reason as above
To calculate m∠3 note that angles 1, 2 and 3 form the three angles of a triangle and their measures must add up to 180°
So
45° + 75° + m∠3 = 180° ==> 120° + m∠3 = 180° or
m∠3 = 180° - 120° = 60° (Blank 3)
Now m∠3 + 79° + m∠4 = 180°
since these angles are adjacent linear angles i.e. they are on the same straight line
Substituting the value for m∠3 = 60° we get
60° + 79° + m∠4 = 180°
==> 139° + m∠4 = 180°
==> m∠4 = 180° - 139° = 41° (Blank 4)
Once again, the three angles ∠4, the angle with measure 68° and ∠5 are the three angles of a triangle so
m∠4 + 68° + m∠5 = 180
==> 41° + 68° + m∠5 = 180°
==> 109° + m∠5
==> m∠5 = 180° - 109° = 71° (Blank 5)
Since ∠5 and ∠6 are adjacent linear angles their sum must be 180°
So we get
m∠5 + m∠6 = 180°
==> 71° + m∠6 = 180°
==> m∠6 = 180° - 71° = 109° (Blank 6)