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Name: ________________________ Class: ___________________ Date: __________ ID: A 4.2 Triangle Sum Theorem Quiz Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find the measure of each numbered angle. a. b. c. d. m∠1 = 54°, m∠2 = 117°, m∠3 = 63° m∠1 = 117°, m∠2 = 63°, m∠3 = 63° m∠1 = 54°, m∠2 = 63°, m∠3 = 63° m∠1 = 54°, m∠2 = 63°, m∠3 = 117° ____ 2. One of the acute angles in a right triangle has a measure of 34.6°. What is the measure of the other acute angle? a. 145.4° b. 34.6° c. 55.4° d. 90° ____ 3. Find m∠DCB, given ∠A ≅ ∠F , ∠B ≅ ∠E , and m∠CDE = 46°. a. b. c. d. m∠DCB = 134° m∠DCB = 67° m∠DCB = 44° m∠DCB = 46° Short Answer 4. The degree measures of the angles of ABC are represented by x, 3x, and 5x − 54. Find the value of x. x = ____________________ 1 ID: A 4.2 Triangle Sum Theorem Quiz Answer Section MULTIPLE CHOICE 1. ANS: C Step 1: ∠2 is supplementary to the angle that is 117°. 117° + m∠2 = 180°. So m∠2 = 63° . Step 2: By the Alternate Interior Angles Theorem, ∠2 ≅ ∠3. So m∠2 = m∠3 = 63° . Step 3: By the Isosceles Triangle Theorem, ∠2 and the angle opposite the other side of the isosceles triangle are congruent. Let ∠4 be that unknown angle. Then, ∠2 ≅ ∠4 and m∠2 = m∠4 = 63° . m∠1 + m∠2 + m∠4 = 180° by the Triangle Sum Theorem. m∠1 + 63° + 63° = 180° . So m∠1 = 54° . Feedback A B C D Angle 2 is supplementary to the angle that measures 117 degrees. To find the measure of angle 1, use the Isosceles Triangle Theorem. Correct! By the Alternate Interior Angles Theorem, angle 2 is congruent to angle 3. PTS: 1 DIF: Advanced REF: 1a9de092-4683-11df-9c7d-001185f0d2ea STA: NY.NYLES.MTH.05.GEO.G.G.30 | NY.NYLES.MTH.05.GEO.G.G.36 LOC: MTH.C.11.03.02.04.002 TOP: 4-8 Isosceles and Equilateral Triangles KEY: multi-step | isosceles triangle theorem DOK: DOK 2 2. ANS: C Let the acute angles be ∠M and ∠N , with m∠M = 34.6°. m∠M + m∠N = 90° The acute angles of a right triangle are complementary. 34.6° + m∠N = 90° Substitute 34.6° for m∠M . m∠N = 55.4° Subtract 34.6° from both sides. Feedback A B C D The two acute angles in a right triangle are complementary. This is the measure of the given angle. Find the measure of the other acute angle. Correct! The measure of the other acute angle is less than 90 degrees. PTS: OBJ: TOP: DOK: 1 DIF: Basic REF: 1a6993ba-4683-11df-9c7d-001185f0d2ea 4-2.2 Finding Angle Measures in Right Triangles LOC: MTH.C.11.03.02.05.001 4-2 Angle Relationships in Triangles KEY: triangle sum theorem DOK 1 1 ID: A 3. ANS: D The Third Angles Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. It is given that ∠A ≅ ∠F and ∠B ≅ ∠E . Therefore, ∠CDE ≅ ∠DCB. So, m∠DCB = 46°. Feedback A B C D This is the supplement. Use the Third Angles Theorem. The Third Angles Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. This is the complement. Use the Third Angles Theorem. Correct! PTS: NAT: TOP: KEY: 1 DIF: Advanced REF: 1a6e5872-4683-11df-9c7d-001185f0d2ea NT.CCSS.MTH.10.9-12.G.SRT.5 LOC: MTH.C.11.03.02.04.005 4-2 Angle Relationships in Triangles third angles theorem | triangle sum theorem DOK: DOK 2 SHORT ANSWER 4. ANS: 26. x + 3x + 5x − 54 = 180 9x = 234 x = 26 PTS: 2 REF: 080933ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles 2 Name: ________________________ Class: ___________________ Date: __________ ID: B 4.2 Triangle Sum Theorem Quiz Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. One of the acute angles in a right triangle has a measure of 18.4°. What is the measure of the other acute angle? a. 161.6° b. 90° c. 71.6° d. 18.4° ____ 2. Find the measure of each numbered angle. a. b. c. d. ____ m∠1 = 117°, m∠2 = 63°, m∠3 = 63° m∠1 = 54°, m∠2 = 117°, m∠3 = 63° m∠1 = 54°, m∠2 = 63°, m∠3 = 117° m∠1 = 54°, m∠2 = 63°, m∠3 = 63° 3. Find m∠DCB, given ∠A ≅ ∠F , ∠B ≅ ∠E , and m∠CDE = 23°. a. b. c. d. m∠DCB = 157° m∠DCB = 67° m∠DCB = 23° m∠DCB = 78.5° Short Answer 4. The degree measures of the angles of ABC are represented by x, 3x, and 5x − 54. Find the value of x. x = ____________________ 1 ID: B 4.2 Triangle Sum Theorem Quiz Answer Section MULTIPLE CHOICE 1. ANS: C Let the acute angles be ∠M and ∠N , with m∠M = 18.4°. m∠M + m∠N = 90° The acute angles of a right triangle are complementary. 18.4° + m∠N = 90° Substitute 18.4° for m∠M . m∠N = 71.6° Subtract 18.4° from both sides. Feedback A B C D The two acute angles in a right triangle are complementary. The measure of the other acute angle is less than 90 degrees. Correct! This is the measure of the given angle. Find the measure of the other acute angle. PTS: 1 DIF: Basic REF: 1a6993ba-4683-11df-9c7d-001185f0d2ea OBJ: 4-2.2 Finding Angle Measures in Right Triangles LOC: MTH.C.11.03.02.05.001 TOP: 4-2 Angle Relationships in Triangles KEY: triangle sum theorem DOK: DOK 1 2. ANS: D Step 1: ∠2 is supplementary to the angle that is 117°. 117° + m∠2 = 180°. So m∠2 = 63° . Step 2: By the Alternate Interior Angles Theorem, ∠2 ≅ ∠3. So m∠2 = m∠3 = 63° . Step 3: By the Isosceles Triangle Theorem, ∠2 and the angle opposite the other side of the isosceles triangle are congruent. Let ∠4 be that unknown angle. Then, ∠2 ≅ ∠4 and m∠2 = m∠4 = 63° . m∠1 + m∠2 + m∠4 = 180° by the Triangle Sum Theorem. m∠1 + 63° + 63° = 180° . So m∠1 = 54° . Feedback A B C D To find the measure of angle 1, use the Isosceles Triangle Theorem. Angle 2 is supplementary to the angle that measures 117 degrees. By the Alternate Interior Angles Theorem, angle 2 is congruent to angle 3. Correct! PTS: STA: LOC: KEY: 1 DIF: Advanced REF: 1a9de092-4683-11df-9c7d-001185f0d2ea NY.NYLES.MTH.05.GEO.G.G.30 | NY.NYLES.MTH.05.GEO.G.G.36 MTH.C.11.03.02.04.002 TOP: 4-8 Isosceles and Equilateral Triangles multi-step | isosceles triangle theorem DOK: DOK 2 1 ID: B 3. ANS: C The Third Angles Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. It is given that ∠A ≅ ∠F and ∠B ≅ ∠E . Therefore, ∠CDE ≅ ∠DCB. So, m∠DCB = 23°. Feedback A B C D This is the supplement. Use the Third Angles Theorem. This is the complement. Use the Third Angles Theorem. Correct! The Third Angles Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. PTS: NAT: TOP: KEY: 1 DIF: Advanced REF: 1a6e5872-4683-11df-9c7d-001185f0d2ea NT.CCSS.MTH.10.9-12.G.SRT.5 LOC: MTH.C.11.03.02.04.005 4-2 Angle Relationships in Triangles third angles theorem | triangle sum theorem DOK: DOK 2 SHORT ANSWER 4. ANS: 26. x + 3x + 5x − 54 = 180 9x = 234 x = 26 PTS: 2 REF: 080933ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles 2 Name: ________________________ Class: ___________________ Date: __________ ID: C 4.2 Triangle Sum Theorem Quiz Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find the measure of each numbered angle. a. b. c. d. m∠1 = 54°, m∠2 = 63°, m∠3 = 63° m∠1 = 117°, m∠2 = 63°, m∠3 = 63° m∠1 = 54°, m∠2 = 117°, m∠3 = 63° m∠1 = 54°, m∠2 = 63°, m∠3 = 117° ____ 2. One of the acute angles in a right triangle has a measure of 37.2°. What is the measure of the other acute angle? a. 52.8° b. 90° c. 37.2° d. 142.8° ____ 3. Find m∠DCB, given ∠A ≅ ∠F , ∠B ≅ ∠E , and m∠CDE = 24°. a. b. c. d. m∠DCB = 24° m∠DCB = 156° m∠DCB = 78° m∠DCB = 66° Short Answer 4. The degree measures of the angles of ABC are represented by x, 3x, and 5x − 54. Find the value of x. x = ____________________ 1 ID: C 4.2 Triangle Sum Theorem Quiz Answer Section MULTIPLE CHOICE 1. ANS: A Step 1: ∠2 is supplementary to the angle that is 117°. 117° + m∠2 = 180°. So m∠2 = 63° . Step 2: By the Alternate Interior Angles Theorem, ∠2 ≅ ∠3. So m∠2 = m∠3 = 63° . Step 3: By the Isosceles Triangle Theorem, ∠2 and the angle opposite the other side of the isosceles triangle are congruent. Let ∠4 be that unknown angle. Then, ∠2 ≅ ∠4 and m∠2 = m∠4 = 63° . m∠1 + m∠2 + m∠4 = 180° by the Triangle Sum Theorem. m∠1 + 63° + 63° = 180° . So m∠1 = 54° . Feedback A B C D Correct! To find the measure of angle 1, use the Isosceles Triangle Theorem. Angle 2 is supplementary to the angle that measures 117 degrees. By the Alternate Interior Angles Theorem, angle 2 is congruent to angle 3. PTS: 1 DIF: Advanced REF: 1a9de092-4683-11df-9c7d-001185f0d2ea STA: NY.NYLES.MTH.05.GEO.G.G.30 | NY.NYLES.MTH.05.GEO.G.G.36 LOC: MTH.C.11.03.02.04.002 TOP: 4-8 Isosceles and Equilateral Triangles KEY: multi-step | isosceles triangle theorem DOK: DOK 2 2. ANS: A Let the acute angles be ∠M and ∠N , with m∠M = 37.2°. m∠M + m∠N = 90° The acute angles of a right triangle are complementary. 37.2° + m∠N = 90° Substitute 37.2° for m∠M . m∠N = 52.8° Subtract 37.2° from both sides. Feedback A B C D Correct! The measure of the other acute angle is less than 90 degrees. This is the measure of the given angle. Find the measure of the other acute angle. The two acute angles in a right triangle are complementary. PTS: OBJ: TOP: DOK: 1 DIF: Basic REF: 1a6993ba-4683-11df-9c7d-001185f0d2ea 4-2.2 Finding Angle Measures in Right Triangles LOC: MTH.C.11.03.02.05.001 4-2 Angle Relationships in Triangles KEY: triangle sum theorem DOK 1 1 ID: C 3. ANS: A The Third Angles Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. It is given that ∠A ≅ ∠F and ∠B ≅ ∠E . Therefore, ∠CDE ≅ ∠DCB. So, m∠DCB = 24°. Feedback A B C D Correct! This is the supplement. Use the Third Angles Theorem. The Third Angles Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. This is the complement. Use the Third Angles Theorem. PTS: NAT: TOP: KEY: 1 DIF: Advanced REF: 1a6e5872-4683-11df-9c7d-001185f0d2ea NT.CCSS.MTH.10.9-12.G.SRT.5 LOC: MTH.C.11.03.02.04.005 4-2 Angle Relationships in Triangles third angles theorem | triangle sum theorem DOK: DOK 2 SHORT ANSWER 4. ANS: 26. x + 3x + 5x − 54 = 180 9x = 234 x = 26 PTS: 2 REF: 080933ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles 2