- e.Unlike the question above, where every complementary angle
must also be acute, supplementary angles can be acute, right, or
obtuse. If an angle is obtuse, its supplement is acute. If an angle is
right, its supplement is also right. Two obtuse angles can never be
a supplementary pair, and two acute angles can never be a
supplementary pair. Without more information, this question
cannot be determined. - e.Complementary angles that are also congruent measure 45°
each. Supplementary angles that are also congruent measure 90°
each. Without more information, this question cannot be
determined. - c. Congruent supplementary angles always measure 90° each:
m∠ABE = x
m∠GIJ = x
m∠ABE + m∠GIJ = 180°; replace each angle with its measure:
x+ x= 180°
2 x= 180°; divide each side by 2:
x= 90°
Any 90° angle is a right angle. - d.When two angles are supplementary to the same angle, they are
congruent to each other:
m∠EDF + m∠HIJ =180°
m∠EDF + m∠SUV = 180°
m∠EDF + m∠HIJ = m∠SUV + m∠EDF; subtract m∠EDF
from each side:
m∠HIJ = m∠SUV
Set 21
- Since ∠ABO is a straight angle, you know that m∠ABO = 180°.
Therefore m∠ABT + m∠TBO = 180°. Since m∠ABT = 125°,
then ∠TBO must equal 55°. - Since ∠BTC is a right angle, you know that m∠BTC = 90°.
Therefore m∠BTO + m∠OTC = 90°. Since m∠BTO = 66°,
then ∠TBO must equal 24°.
501 Geometry Questions