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This document contains 12 geometry problems involving properties of polygons such as parallelograms, triangles, and trapezoids. The problems ask the learner to determine missing angle measures using facts about interior and exterior angles, angle sums in polygons and triangles, and properties of parallel lines cut by a transversal. Sample problems include finding an exterior angle measure given interior angles in a parallelogram (problem 1) and determining an angle measure using the fact that opposite angles in a parallelogram are congruent (problem 10).

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Aldrin Bagasina
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70 views6 pages

1 Xps

This document contains 12 geometry problems involving properties of polygons such as parallelograms, triangles, and trapezoids. The problems ask the learner to determine missing angle measures using facts about interior and exterior angles, angle sums in polygons and triangles, and properties of parallel lines cut by a transversal. Sample problems include finding an exterior angle measure given interior angles in a parallelogram (problem 1) and determining an angle measure using the fact that opposite angles in a parallelogram are congruent (problem 10).

Uploaded by

Aldrin Bagasina
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Regents Exam Questions Name: ________________________

G.CO.C.11: Interior and Exterior Angles of Polygons 1


www.jmap.org

G.CO.C.11: Interior and Exterior Angles of Polygons 1

1 In the diagram of parallelogram FRED shown 3 In parallelogram PQRS, QP is extended to point T


below, ED is extended to A, and AF is drawn such and ST is drawn.
that AF ≅ DF .

If ST ≅ SP and m∠R = 130° , what is m∠PST ?


If m∠R = 124° , what is m∠AFD ? 1) 130°
1) 124° 2) 80°
2) 112° 3) 65°
3) 68° 4) 50°
4) 56°

4 In the diagram below of parallelogram ROCK,


2 In the diagram below, ABCD is a parallelogram, m∠C is 70° and m∠ROS is 65°.
AB is extended through B to E, and CE is drawn.

What is m∠KSO ?
If CE ≅ BE and m∠D = 112° , what is m∠E ? 1) 45º
1) 44° 2) 110º
2) 56° 3) 115º
3) 68° 4) 135º
4) 112°

1
Regents Exam Questions Name: ________________________
G.CO.C.11: Interior and Exterior Angles of Polygons 1
www.jmap.org

5 In parallelogram ABCD shown below, EB bisects 7 In the diagram below of parallelogram ABCD,
∠ABC . AFGB, CF bisects ∠DCB, DG bisects ∠ADC , and
CF and DG intersect at E.

If m∠A = 40° , then m∠BED is


1) 40°
2) 70°
3) 110° If m∠B = 75° , then the measure of ∠EFA is
4) 140° 1) 142.5°
2) 127.5°
3) 52.5°
4) 37.5°
6 In parallelogram QRST shown below, diagonal TR
is drawn, U and V are points on TS and QR,
respectively, and UV intersects TR at W.
8 Quadrilateral EBCF and AD are drawn below, such
that ABCD is a parallelogram, EB ≅ FB , and
EF ⊥FH .

If m∠S = 60° , m∠SRT = 83° , and m∠TWU = 35° ,


what is m∠WVQ ?
1) 37º
2) 60º
3) 72º
4) 83º

If m∠E = 62° and m∠C = 51° , what is m∠FHB ?


1) 79º
2) 76º
3) 73º
4) 62º

2
Regents Exam Questions Name: ________________________
G.CO.C.11: Interior and Exterior Angles of Polygons 1
www.jmap.org

9 The diagram below shows parallelogram LMNO 11 Parallelogram ABCD is adjacent to rhombus
with diagonal LN , m∠M = 118° , and DEFG, as shown below, and FC intersects AGD at
m∠LNO = 22° . H.

Explain why m∠NLO is 40 degrees.

10 In parallelogram ABCD shown below,


m∠DAC = 98° and m∠ACD = 36° .

If m∠B = 118° and m∠AHC = 138° , determine and


state m∠GFH .

What is the measure of angle B? Explain why. 12 Trapezoid ABCD, where AB  CD, is shown below.
Diagonals AC and DB intersect MN at E, and
AD ≅ AE .

If m∠DAE = 35° , m∠DCE = 25° , and


m∠NEC = 30° , determine and state m∠ABD .

3
ID: A

G.CO.C.11: Interior and Exterior Angles of Polygons 1


Answer Section

1 ANS: 3

REF: 081508geo
2 ANS: 1
180 − (68 ⋅ 2)

REF: 081624geo
3 ANS: 2

REF: 061921geo
4 ANS: 4

REF: 081708geo
5 ANS: 3

REF: 082215geo
6 ANS: 3

REF: 011603geo

1
ID: A

7 ANS: 2

REF: 081907geo
8 ANS: 1

m∠CBE = 180 − 51 = 129

REF: 062221geo
9 ANS:
Opposite angles in a parallelogram are congruent, so m∠O = 118° . The interior angles of a triangle equal 180°.
180 − (118 + 22) = 40.

REF: 061526geo
10 ANS:
∠D = 46° because the angles of a triangle equal 180°. ∠B = 46° because opposite angles of a parallelogram are
congruent.

REF: 081925geo
11 ANS:

20º

REF: 011926geo

2
ID: A

12 ANS:

47.5°

REF: 082230geo

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