1. There is one angle measure such that doubling its complement would yield the same as adding 30 to one-fourth of its supplement. Find the measure of the angle using algebra. Be sure to check the answer.
2. Find as many errors as you can in the following proof and correct them. You may have to insert steps too.
Given: Segment QR is perpendicular to segment SR... Segment RS is perpendicular to Segment ST and angle 2 and angle 3 are complementary
Prove: Angle 1 and Angle 4 are complementary
Statements Reasons
1. QR perpendicular to SR 1. Given
RS perpendicular to ST
Angle 2 Angle 3 are complementary
2. Measure of angle QRS = 90 2. Definition of Perpendicular LInes
Measure of angle TSR = 90
3. Measure of angle 2 + measure of angle 3 = 90 3. Definition of complementary angles.
4. m angle 1 + m angle 2 = 90 4. Angle add'n postulate
m angle 3 + m angle 4 = 90
5. m angle qrs = m angle tsr 5. Substitution
6. m angle 1 + m angle 2 = 6. Subst.
m angle 3 + m angle 4
7. m angle 1 + m angle 2 + m angle 3 + m angle 4 = 180 7. Angle Addition Postulate
8. m angle 1 +90 + m angle 4 =180 8. Subst.
9. m angle 1 + m angle 4 = 90 9. Alg.
10. angle 1 and angle 4 are complementary 10. defn right angle
3. The perimeter of a parallelogram is 140 units. What are its dimensions if the lengths of the adjacent sides are in the ratio 7 to 5?
4. Draw triangle ABC showing angle abc bisected by segment BY and angle ACB bisected by CX. Let D be the point of intersection of BY and CX. IF angle ABC = angle ACB then prove that angle DBC = angle DCB
5. Two angles are supplementary. Three-fourths of the larger angle is one less than two-thirds of the smaller angle. Find the measure of each angle using algebra. Be sure to check your answer.
6. Given: Angle ABC is a right angle
Angle DEF is a right angle
Angle 1 = angle 3
Prove: angle 2 = angle 4
7. Given BE = CD
Prove: BD = EC
8. Two parallel lines are cut by a transversal. A pair of alternate exterior angles has measurements such that the square of one angle is four times the difference of two times the angle and three. If possible, use algebra to find an angle(s) that meets this description.
9.A pair of same side interior angles are trisected by lines m, n , p and q. Find out what you can about the angles of ABCD
10. Find the sum of the measures of the angles formed at the tips of each star.
c. using inductive reasoning, suggest a formula for the sum of the angle measures at the tips of an n pointed star.
d. using deductive reasoning, justify your formula.
2. Find as many errors as you can in the following proof and correct them. You may have to insert steps too.
Given: Segment QR is perpendicular to segment SR... Segment RS is perpendicular to Segment ST and angle 2 and angle 3 are complementary
Prove: Angle 1 and Angle 4 are complementary
Statements Reasons
1. QR perpendicular to SR 1. Given
RS perpendicular to ST
Angle 2 Angle 3 are complementary
2. Measure of angle QRS = 90 2. Definition of Perpendicular LInes
Measure of angle TSR = 90
3. Measure of angle 2 + measure of angle 3 = 90 3. Definition of complementary angles.
4. m angle 1 + m angle 2 = 90 4. Angle add'n postulate
m angle 3 + m angle 4 = 90
5. m angle qrs = m angle tsr 5. Substitution
6. m angle 1 + m angle 2 = 6. Subst.
m angle 3 + m angle 4
7. m angle 1 + m angle 2 + m angle 3 + m angle 4 = 180 7. Angle Addition Postulate
8. m angle 1 +90 + m angle 4 =180 8. Subst.
9. m angle 1 + m angle 4 = 90 9. Alg.
10. angle 1 and angle 4 are complementary 10. defn right angle
3. The perimeter of a parallelogram is 140 units. What are its dimensions if the lengths of the adjacent sides are in the ratio 7 to 5?
4. Draw triangle ABC showing angle abc bisected by segment BY and angle ACB bisected by CX. Let D be the point of intersection of BY and CX. IF angle ABC = angle ACB then prove that angle DBC = angle DCB
5. Two angles are supplementary. Three-fourths of the larger angle is one less than two-thirds of the smaller angle. Find the measure of each angle using algebra. Be sure to check your answer.
6. Given: Angle ABC is a right angle
Angle DEF is a right angle
Angle 1 = angle 3
Prove: angle 2 = angle 4
7. Given BE = CD
Prove: BD = EC
8. Two parallel lines are cut by a transversal. A pair of alternate exterior angles has measurements such that the square of one angle is four times the difference of two times the angle and three. If possible, use algebra to find an angle(s) that meets this description.
9.A pair of same side interior angles are trisected by lines m, n , p and q. Find out what you can about the angles of ABCD
10. Find the sum of the measures of the angles formed at the tips of each star.
c. using inductive reasoning, suggest a formula for the sum of the angle measures at the tips of an n pointed star.
d. using deductive reasoning, justify your formula.
