Consequently, in consecutive order, the angles measure 180°−21°,
or 159°, 21°, and 159°. Choice bdoes not align the angles in
consecutive order; choice cmistakenly subtracts 21° from 90° when
consecutive angles are supplementary, not complementary.- c.Opposite angles in an isosceles trapezoid are supplementary.
Choice adescribes a consecutive angle along the same parallel line. - d.XZis a diagonal in rectangle WXYZ. ∠WXZ and ∠XZY are
alternate interior angles along the diagonal; they are congruent;
and when they are added with their adjacent angle, the two angles
form a 90° angle. - a.BDis a diagonal in square ABCD. It bisects vertices B and D,
creating four congruent 45° angles. Choice bis incorrect because
∠ABD is half of ∠ADC; they are not congruent. Choice cis
incorrect because when two 45° angles are added together they
measure 90°, not 180°. - e.It cannot be determined.
Set 54
- First, opposite sides of a rhombus are parallel, which means
alternate interior angles are congruent. If ∠BCA measurements
72°, then ∠CAD also measures 72°. The sum of the measurements
of all three interior angles of a triangle must equal 180°: 72° + 18° +
m∠AOB = 180°. m∠AOD = 90°. Because ACand DBare
intersecting straight lines, if one angle of intersection measures
90°, all four angles of intersection measure 90°, which means the
lines perpendicularly meet. - a= 4 5 . BPis the height of rhombus ABCD and the leg of
ΔBPC. Use the Pythagorean theorem: a^2 + 8^2 = 12^2. a^2 + 64 = 144.
a^2 = 80. a= 4 5 . - c= 4 30 .Use the Pythagorean theorem to find the hypotenuse of
ΔBPD, which is diagonal BD: (4 5 )^2 + (12 + 8)^2 = c^2.
80 + 400 = c^2. 480 = c^2. 4 30 = c.
501 Geometry Questions