GEOMETRY SEMESTER TEST
8 sides - correct answer How many sides does a regular polygon have if each exterior angle measures 45?
91 - correct answer The sum of the measures of two exterior angles of a triangle is 269. What is the measure of the third exterior angle?
4680 - correct answer What is the sum of the interior angle measures of a 28-gon?
17 - correct answer The sum of the interior angle measures of a polygon with "s" sides is 2700. Find "s"
x = 123, y = 58 - correct answer Find the missing values of the variables. #5
144 - correct answer A road sign is in the shape of a regular decagon. What is the measure of each interior angle on the sign? Round to the nearest tenth.
m<1 = 18, m<3 = 72 - correct answer Find m<1 and m<3 in the kite. #7
20 - correct answer m<R = 140 and m<S =100. Find m<T. #8
63, 117 - correct answer The isosceles trapezoid is part of an isosceles triangle with a 54 degree vertex angle. What is the measure of an acute base angle of the trapezoid? Of an obtuse base angle? #9
34 - correct answer LM is the midsegment of ABCD. AB = x + 8, LM = 4x +3, and DC =
236. What is the value of x? #10
104 - correct answer ABCD is a parallelogram. If m<DAB = 104, then m<BCD = ? #11
103 - correct answer ABCD is a parallelogram. If m<CDA = 77, then m<DAB = ? #12
x = 15, y = 10 - correct answer In parallelogram DEFG, DH = x + 5, HF = 2y, GH = 2x -
5, and HE = 2y + 5. Find the value of x and y. #14
x = 9, NM = 51, OL = 51 - correct answer LMNO is a parallelogram. if NM = x + 42 and
OL = 5x + 6, find the value of x then find NM and OL. #13
6 - correct answer Find AM in the parallelogram if PN = 15 and AO = 6. #15
x = 11, y = 11/3 - correct answer If ON = 5x - 7, LM = 4x +4, NM = x - 7, and OL = 3y - 7, find the values of x and y for which LMNO must be a parallelogram. #16 Yes; both pairs of opposite sides are congruent. - correct answer Based on the information in the diagram, can you prove that the figure is the parallelogram? Explain. #17
Yes; opposite sides are congruent. - correct answer Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. #18
300 - correct answer If m<B = m<D = 30, find m<C so that quadrilateral ABCD is a parallelogram. #19
x = 50, PR = 781, QS = 781 - correct answer In rectangle PQRS, PR = 16x - 19 and QS = x + 731. Find the value of x and the length of each diagonal. #20
x = 10, DF = 57, EG = 57 - correct answer DEFG is a rectangle. DF = 6x - 3 and EG = x + 47. Find the value of each diagonal.
m<2 = 154, m<3 = 13 - correct answer In the rhombus, m<1 = 154. What are m<2 and m<3? #22
m<1 = 90, m<2 = 25, and m<3 = 65 - correct answer Find the measure of the numbered angles in the rhombus. #23
48 - correct answer What is XZ? #24
4 - correct answer In quadrilateral ABCD, m<ACD = 2x + 4 and m<ACB = 5x - 8. For what value of x is ABCD a rhombus? #25
Parallelogram ABCD is a rhombus, because the diagonal bisects two angles. - correct answer Parallelogram ABCD has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain. #26
12 - correct answer In quadrilateral ABCD, AE = x = 6 and BE = 3x -18. For what value
of x is ABCD a rectangle? #27
<B; DC - correct answer A. <H = ? B. GH/DJ = AB/? #28
A' (-3,6), B' (6,3) C' (-6,-6) - correct answer What are the vertices of D1.5 #29
x = 9 - correct answer The polygons are similar, but not necessarily drawn to scale. Find the value of x. #30
x = 13 - correct answer The polygons are similar, but not necessarily drawn to scale. Find the value of x. #31
8 sides - correct answer How many sides does a regular polygon have if each exterior angle measures 45?
91 - correct answer The sum of the measures of two exterior angles of a triangle is 269. What is the measure of the third exterior angle?
4680 - correct answer What is the sum of the interior angle measures of a 28-gon?
17 - correct answer The sum of the interior angle measures of a polygon with "s" sides is 2700. Find "s"
x = 123, y = 58 - correct answer Find the missing values of the variables. #5
144 - correct answer A road sign is in the shape of a regular decagon. What is the measure of each interior angle on the sign? Round to the nearest tenth.
m<1 = 18, m<3 = 72 - correct answer Find m<1 and m<3 in the kite. #7
20 - correct answer m<R = 140 and m<S =100. Find m<T. #8
63, 117 - correct answer The isosceles trapezoid is part of an isosceles triangle with a 54 degree vertex angle. What is the measure of an acute base angle of the trapezoid? Of an obtuse base angle? #9
34 - correct answer LM is the midsegment of ABCD. AB = x + 8, LM = 4x +3, and DC =
236. What is the value of x? #10
104 - correct answer ABCD is a parallelogram. If m<DAB = 104, then m<BCD = ? #11
103 - correct answer ABCD is a parallelogram. If m<CDA = 77, then m<DAB = ? #12
x = 15, y = 10 - correct answer In parallelogram DEFG, DH = x + 5, HF = 2y, GH = 2x -
5, and HE = 2y + 5. Find the value of x and y. #14
x = 9, NM = 51, OL = 51 - correct answer LMNO is a parallelogram. if NM = x + 42 and
OL = 5x + 6, find the value of x then find NM and OL. #13
6 - correct answer Find AM in the parallelogram if PN = 15 and AO = 6. #15
x = 11, y = 11/3 - correct answer If ON = 5x - 7, LM = 4x +4, NM = x - 7, and OL = 3y - 7, find the values of x and y for which LMNO must be a parallelogram. #16 Yes; both pairs of opposite sides are congruent. - correct answer Based on the information in the diagram, can you prove that the figure is the parallelogram? Explain. #17
Yes; opposite sides are congruent. - correct answer Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. #18
300 - correct answer If m<B = m<D = 30, find m<C so that quadrilateral ABCD is a parallelogram. #19
x = 50, PR = 781, QS = 781 - correct answer In rectangle PQRS, PR = 16x - 19 and QS = x + 731. Find the value of x and the length of each diagonal. #20
x = 10, DF = 57, EG = 57 - correct answer DEFG is a rectangle. DF = 6x - 3 and EG = x + 47. Find the value of each diagonal.
m<2 = 154, m<3 = 13 - correct answer In the rhombus, m<1 = 154. What are m<2 and m<3? #22
m<1 = 90, m<2 = 25, and m<3 = 65 - correct answer Find the measure of the numbered angles in the rhombus. #23
48 - correct answer What is XZ? #24
4 - correct answer In quadrilateral ABCD, m<ACD = 2x + 4 and m<ACB = 5x - 8. For what value of x is ABCD a rhombus? #25
Parallelogram ABCD is a rhombus, because the diagonal bisects two angles. - correct answer Parallelogram ABCD has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain. #26
12 - correct answer In quadrilateral ABCD, AE = x = 6 and BE = 3x -18. For what value
of x is ABCD a rectangle? #27
<B; DC - correct answer A. <H = ? B. GH/DJ = AB/? #28
A' (-3,6), B' (6,3) C' (-6,-6) - correct answer What are the vertices of D1.5 #29
x = 9 - correct answer The polygons are similar, but not necessarily drawn to scale. Find the value of x. #30
x = 13 - correct answer The polygons are similar, but not necessarily drawn to scale. Find the value of x. #31
