Geometry Mathematical Reasoning

Question

If two lines intersect and one of the angles formed has a measure of 67 degrees, which of the following statements are true?

1. Vertical angles are congruent; therefore another angle must equal 67 degrees

1. The lines form linear pairs

1. One of the angles formed measures 23 degrees

1. Two of the angles formed measure 113 degrees

1. Two of the angles formed will have a sum of 180

1. None of the above

Answer 1

When two lines intersect they will create 4 angles; two pairs of congruent angles and two pairs of supplementary angles (sum of 180). If one angle is 67 then another angle is also 67. Two other angles will also be supplementary to 67. x+67=180 will give you their measurements. x=113.

1. Vertical angles are congruent; therefore another angle must equal 67 degrees (TRUE)

1. The lines form linear pairs (TRUE)

1. One of the angles formed measures 23 degrees (FALSE)

1. Two of the angles formed measure 113 degrees (TRUE)

1. Two of the angles formed will have a sum of 180  (TRUE)

1. None of the above (FALSE)

Answer 2

another angle formed will be 67 degrees

two other angles formed will = 180-67 = 113 degrees

two angles formed will sum to 180 (67+113 = 180)

all statements are true, except the last 'none of the above"