All HiSET: Math Resources
Example Questions
Example Question #71 : Hi Set: High School Equivalency Test: Math
and
are a pair of vertical angles.
and
are a linear pair.
and
are the two acute angles of a right triangle.
Which of the following must be true?
Possible Answers:
Correct answer:
Explanation:
and
are a pair of vertical angles; it follows that
and
are a linear pair; it follows that they are supplementary - that is,
.
and
are the two acute angles of a right triangle; it follows that they are complementary - that is,
.
Therefore, we have the three statements
From the second statement, we can subtract from both sides to get
Substitute this expression for in the third expression to get
Substitute for
:
Add to both sides:
,
or, rearranged,
.
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