Answers
Set 19
- c. ∠NOM and ∠LOP are opposite angles formed by intersecting
lines NR and MK; thus, they are vertical angles. - d.∠TLK and ∠MLS are opposite angles formed by intersecting
lines TS and MK; thus, they are vertical angles. - a. ∠MOR and ∠NOK are both adjacent to ∠NOM along two
different lines. The measurement of each angle added to the
measurement of ∠NOM equals that of a straight line, or 180°.
Each of the other answer choices is supplementary to each other,
but not to ∠NOM. - c. ∠1 is the vertical angle to ∠TLK, which is given. ∠2 is the
vertical pair to ∠NOM, which is also given. Since vertical angles
are congruent, ∠1 and ∠2 measure 42° and 97°, respectively. To
find the measure of ∠3, subtract the sum of ∠1 and ∠2 from 180°
(the sum of the measurement of a triangle’s interior angles):
180° – (42° + 97°) = m∠ 3
41° = m∠ 3 - a. There are two ways to find the measurement of exterior angle
OPS. The first method subtracts the measurement of ∠3 from
180°. The second method adds the measurements of ∠1 and ∠ 2
together because the measurement of an exterior angle equals the
sum of the two nonadjacent interior angles. ∠OPS measures 139°.
Set 20
- a. The sum of any two complementary angles must equal 90°.
Any angle less than 90° is acute. It only makes sense that the
measurement of two acute angles could add to 90°. Choice b
assumes both angles are also congruent; however, that information
is not given. If the measurement of one obtuse angle equals more
than 90°, then two obtuse angles could not possibly measure
exactly 90° together. Choices cand dare incorrect.
501 Geometry Questions