Geometry · Unit 2
Name an acute angle, an obtuse angle, a complementary pair, a supplementary pair, an adjacent pair, and the parallel lines.
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Size
Acute: less than 90°.
Right: 90°. A square marks it.
Obtuse: greater than 90° and less than 180°.
Pairs
Adjacent angles share a vertex and a side. Their interiors do not overlap.
Complementary angles add to 90°.
Supplementary angles add to 180°. A linear pair is adjacent and supplementary.
A shared side is not enough
Two angles can share a ray and still not be supplementary.
Check the sum, or check that the outer sides form a line.
Arrow marks
Matching arrow marks mean those lines are parallel.
A line with no arrow mark is not marked parallel to them.
The measure is on the diagram.
Not drawn to scale.
1. Which numbered angle is acute?
2. Which numbered angle is obtuse?
3. Which numbered angle is right?
4. Which lines are parallel?
1. Angle 1 is 28°. That is less than 90°, so it is acute.
2. Angle 2 is 152°. That is between 90° and 180°, so it is obtuse.
3. Angle 3 is 90°. The square marks a right angle.
4. m and n have matching arrow marks, so m ∥ n. Line p has no arrow mark.
Answer: 1 acute; 2 obtuse; 3 right; m ∥ n
Not drawn to scale.
1. Which numbered angle is acute?
2. Which numbered angle is obtuse?
3. Which numbered angle is right?
4. Which lines are parallel?
1. Angle 1 is 41°. That is less than 90°, so it is acute.
2. Angle 2 is 139°. That is between 90° and 180°, so it is obtuse.
3. Angle 3 is 90°. The square marks a right angle.
4. m and p have matching arrow marks, so m ∥ p. Line n has no arrow mark.
Answer: 1 acute; 2 obtuse; 3 right; m ∥ p
Not drawn to scale.
1. Which numbered angle is acute?
2. Which numbered angle is obtuse?
3. Which numbered angle is right?
4. Which lines are parallel?
1. Angle 1 is 17°. That is less than 90°, so it is acute.
2. Angle 2 is 163°. That is between 90° and 180°, so it is obtuse.
3. Angle 3 is 90°. The square marks a right angle.
4. n and p have matching arrow marks, so n ∥ p. Line m has no arrow mark.
Answer: 1 acute; 2 obtuse; 3 right; n ∥ p
Not drawn to scale.
1. Which numbered angle is acute?
2. Which numbered angle is obtuse?
3. Which numbered angle is right?
4. Which lines are parallel?
1. Angle 1 is 65°. That is less than 90°, so it is acute.
2. Angle 2 is 115°. That is between 90° and 180°, so it is obtuse.
3. Angle 3 is 90°. The square marks a right angle.
4. m and n have matching arrow marks, so m ∥ n. Line p has no arrow mark.
Answer: 1 acute; 2 obtuse; 3 right; m ∥ n
Not drawn to scale.
1. Which numbered angle is acute?
2. Which numbered angle is obtuse?
3. Which numbered angle is right?
4. Which lines are parallel?
1. Angle 1 is 33°. That is less than 90°, so it is acute.
2. Angle 2 is 147°. That is between 90° and 180°, so it is obtuse.
3. Angle 3 is 90°. The square marks a right angle.
4. m and p have matching arrow marks, so m ∥ p. Line n has no arrow mark.
Answer: 1 acute; 2 obtuse; 3 right; m ∥ p
Not drawn to scale.
1. Which numbered angle is acute?
2. Which numbered angle is obtuse?
3. Which numbered angle is right?
4. Which lines are parallel?
1. Angle 1 is 54°. That is less than 90°, so it is acute.
2. Angle 2 is 126°. That is between 90° and 180°, so it is obtuse.
3. Angle 3 is 90°. The square marks a right angle.
4. n and p have matching arrow marks, so n ∥ p. Line m has no arrow mark.
Answer: 1 acute; 2 obtuse; 3 right; n ∥ p
Pairs, from one figure.
Not drawn to scale.
Angle 1 is 37°, so it is acute. Angles 3 and 4 are also acute.
Angle 2 is 143°, so it is obtuse.
Angles 3 and 4 make a right angle: 58° + 32° = 90°. They are complementary.
Angles 1 and 2 form a straight line: 37° + 143° = 180°. They are supplementary.
Angles 1 and 2 are adjacent. Angles 3 and 4 are adjacent too.
m and n have matching arrow marks, so m ∥ n. Line k does not.
Answer: acute 1; obtuse 2; complementary 3 and 4; supplementary 1 and 2; adjacent 1 and 2; m ∥ n
Not drawn to scale.
Angle 1 is 42°, so it is acute. Angles 3 and 4 are also acute.
Angle 2 is 138°, so it is obtuse.
Angles 3 and 4 make a right angle: 25° + 65° = 90°. They are complementary.
Angles 1 and 2 form a straight line: 42° + 138° = 180°. They are supplementary.
Angles 1 and 2 are adjacent. Angles 3 and 4 are adjacent too.
m and n have matching arrow marks, so m ∥ n. Line k does not.
Answer: acute 1; obtuse 2; complementary 3 and 4; supplementary 1 and 2; adjacent 1 and 2; m ∥ n
Not drawn to scale.
Angle 1 is 29°, so it is acute. Angles 3 and 4 are also acute.
Angle 2 is 151°, so it is obtuse.
Angles 3 and 4 make a right angle: 61° + 29° = 90°. They are complementary.
Angles 1 and 2 form a straight line: 29° + 151° = 180°. They are supplementary.
Angles 1 and 2 are adjacent. Angles 3 and 4 are adjacent too.
m and n have matching arrow marks, so m ∥ n. Line k does not.
Answer: acute 1; obtuse 2; complementary 3 and 4; supplementary 1 and 2; adjacent 1 and 2; m ∥ n
Not drawn to scale.
Angle 1 is 51°, so it is acute. Angles 3 and 4 are also acute.
Angle 2 is 129°, so it is obtuse.
Angles 3 and 4 make a right angle: 22° + 68° = 90°. They are complementary.
Angles 1 and 2 form a straight line: 51° + 129° = 180°. They are supplementary.
Angles 1 and 2 are adjacent. Angles 3 and 4 are adjacent too.
m and n have matching arrow marks, so m ∥ n. Line k does not.
Answer: acute 1; obtuse 2; complementary 3 and 4; supplementary 1 and 2; adjacent 1 and 2; m ∥ n
Not drawn to scale.
Angle 1 is 33°, so it is acute. Angles 3 and 4 are also acute.
Angle 2 is 147°, so it is obtuse.
Angles 3 and 4 make a right angle: 64° + 26° = 90°. They are complementary.
Angles 1 and 2 form a straight line: 33° + 147° = 180°. They are supplementary.
Angles 1 and 2 are adjacent. Angles 3 and 4 are adjacent too.
m and n have matching arrow marks, so m ∥ n. Line k does not.
Answer: acute 1; obtuse 2; complementary 3 and 4; supplementary 1 and 2; adjacent 1 and 2; m ∥ n
Not drawn to scale.
Angle 1 is 46°, so it is acute. Angles 3 and 4 are also acute.
Angle 2 is 134°, so it is obtuse.
Angles 3 and 4 make a right angle: 18° + 72° = 90°. They are complementary.
Angles 1 and 2 form a straight line: 46° + 134° = 180°. They are supplementary.
Angles 1 and 2 are adjacent. Angles 3 and 4 are adjacent too.
m and n have matching arrow marks, so m ∥ n. Line k does not.
Answer: acute 1; obtuse 2; complementary 3 and 4; supplementary 1 and 2; adjacent 1 and 2; m ∥ n
A shared ray does not make a pair supplementary.
Not drawn to scale.
1. Are ∠ABC and ∠CBD supplementary?
2. Are ∠ABC and ∠CBE supplementary?
3. Name an adjacent pair.
4. Which lines are parallel?
1. Yes. They form a straight line: 68° + 112° = 180°.
2. No. 68° + 68° = 136°, which is not 180°. Sharing ray BC is not enough.
3. ∠ABC and ∠CBD are adjacent. ∠ABC and ∠CBE are adjacent too. The second pair is congruent, and it is not supplementary.
4. m and n have matching arrow marks, so m ∥ n. Line p does not.
Answer: yes; no; ∠ABC and ∠CBD; m ∥ n
Not drawn to scale.
1. Are ∠ABC and ∠CBD supplementary?
2. Are ∠ABC and ∠CBE supplementary?
3. Name an adjacent pair.
4. Which lines are parallel?
1. Yes. They form a straight line: 41° + 139° = 180°.
2. No. 41° + 41° = 82°, which is not 180°. Sharing ray BC is not enough.
3. ∠ABC and ∠CBD are adjacent. ∠ABC and ∠CBE are adjacent too. The second pair is congruent, and it is not supplementary.
4. m and n have matching arrow marks, so m ∥ n. Line p does not.
Answer: yes; no; ∠ABC and ∠CBD; m ∥ n
Not drawn to scale.
1. Are ∠ABC and ∠CBD supplementary?
2. Are ∠ABC and ∠CBE supplementary?
3. Name an adjacent pair.
4. Which lines are parallel?
1. Yes. They form a straight line: 75° + 105° = 180°.
2. No. 75° + 30° = 105°, which is not 180°. Sharing ray BC is not enough.
3. ∠ABC and ∠CBD are adjacent. ∠ABC and ∠CBE are adjacent too. The second pair is not congruent, and it is not supplementary.
4. m and n have matching arrow marks, so m ∥ n. Line p does not.
Answer: yes; no; ∠ABC and ∠CBD; m ∥ n
Not drawn to scale.
1. Are ∠ABC and ∠CBD supplementary?
2. Are ∠ABC and ∠CBE supplementary?
3. Name an adjacent pair.
4. Which lines are parallel?
1. Yes. They form a straight line: 23° + 157° = 180°.
2. No. 23° + 23° = 46°, which is not 180°. Sharing ray BC is not enough.
3. ∠ABC and ∠CBD are adjacent. ∠ABC and ∠CBE are adjacent too. The second pair is congruent, and it is not supplementary.
4. m and n have matching arrow marks, so m ∥ n. Line p does not.
Answer: yes; no; ∠ABC and ∠CBD; m ∥ n
Not drawn to scale.
1. Are ∠ABC and ∠CBD supplementary?
2. Are ∠ABC and ∠CBE supplementary?
3. Name an adjacent pair.
4. Which lines are parallel?
1. Yes. They form a straight line: 54° + 126° = 180°.
2. No. 54° + 80° = 134°, which is not 180°. Sharing ray BC is not enough.
3. ∠ABC and ∠CBD are adjacent. ∠ABC and ∠CBE are adjacent too. The second pair is not congruent, and it is not supplementary.
4. m and n have matching arrow marks, so m ∥ n. Line p does not.
Answer: yes; no; ∠ABC and ∠CBD; m ∥ n
Not drawn to scale.
1. Are ∠ABC and ∠CBD supplementary?
2. Are ∠ABC and ∠CBE supplementary?
3. Name an adjacent pair.
4. Which lines are parallel?
1. Yes. They form a straight line: 36° + 144° = 180°.
2. No. 36° + 36° = 72°, which is not 180°. Sharing ray BC is not enough.
3. ∠ABC and ∠CBD are adjacent. ∠ABC and ∠CBE are adjacent too. The second pair is congruent, and it is not supplementary.
4. m and n have matching arrow marks, so m ∥ n. Line p does not.
Answer: yes; no; ∠ABC and ∠CBD; m ∥ n
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