Geometry Homework Practice Workbook 1st Edition Chapter 2 Inductive Reasoning and Conjecture
Geometry Homework Practice Workbook 1st Edition Chapter 2 Exercise 2.8 Solutions Page 29 Problem 1 Answer
We are given a figure, in which m∠5=22 and one angle measures 90.
We are required to find the measure of m∠6.
Here, we will use the fact that the total sum of angles that lie on a line is 180.
As all the angles lie on the same line, by angles on a straight line property we have,
90+m∠5+m∠6=180
90+22+m∠6=180
m∠6=180−112
m∠6=68
In the given figure, by angles on a straight line property, we have m∠6=68 when m∠5=22.
Read and Learn More Geometry, Homework Practice Workbook 1st Edition Solutions
Solutions For Inductive Reasoning And Conjecture Exercise 2.8 Page 29 Problem 2 Answer
Page 29 Problem 3 Answer
In the question, we have been given a figure and also we have:
m∠13=4x+11
m∠14=3x+1
We have been asked to find the measure of each numbered angle and name the theorems that justify our work.
Using the linear pair theorem, we will find the result.
Here in the given figure, by the linear pair, we get
∠13+∠14=180∘
4x+11+3x+1=180∘
7x=180−12
x=168/7
x=24∘
Now substituting the value of x=24∘ in the angles, we get
m∠13=4×24+11
=107∘m∠14=3×24+1
=73∘
So, by linear pair theorem, we get the measure of each angle.
Hence we get the measure of each angle by the linear pair in the given figuer as:
m∠13=107∘
m∠14=73∘
Geometry Workbook 1st Edition Exercise 2.8 Solutions Page 29 Problem 4 Answer
We have been given that in the given figure, ∠9,∠10 are complementary angles, ∠7 congruent to ∠9, m∠8=41.
We have to find the measure of each angle.
Using the linear pair theorem, we will get the measure.
By the linear pair, we get
∠7+∠8+∠9+∠10=180
∠7+41+90=180
∠7=49
Now given that ∠7≅∠9.
Thus we get 49∘=∠9.
Also, we have given that ∠9,∠10 are complementary angles.
Thus we get
∠9+∠10=90∘
49+∠10=90∘
∠10=41∘
So, we get the measure of all the angles.
Hence we get the measure of all the angles in the figure as: ∠7=49∘
by linear pair ∠10=41∘
by complement ∠9=49∘by congruence
Inductive Reasoning And Conjecture Solutions Chapter 2 Exercise 2.8 Geometry Workbook Page 29 Problem 5 Answer
In the question, we have been given a figure and also given that ∠QPS≅∠TPR and also an incomplete table.
We have to complete the table with the proof of ∠QPR≅∠TPS.
Using the given information and figure we will complete it.
Here the complete table is:
Hence with the help of the given figure, we had completed the table and proved that ∠QPR≅∠TPS
Step-By-Step Solutions For Geometry Homework Practice Workbook Chapter 2 Exercise 2.8 Page 30 Problem 6 Answer
Here, we have given a figure in which a straight line is divided by a line into two angles, that are ∠1,∠2.Further, we have given
m∠1=x+10
m∠2=3x+18.
Thus we just have to find the value of m∠1,m∠2.
As we have given
m∠1=x+10……(1)
m∠2=3x+18……(2)
So we also know according to the property of straight line,m∠1+m∠2=180∘
i.e.x+10+3x+18=180∘
4x+28=180∘
4x=180−28
x=152/4
We get
x=38∘
Now putting x in eq. 1 and 2, we will have
m∠1=x+10
=38+10
=48∘and
m∠2=3x+18
=3⋅38+18
=114+18
=132∘
Hence by solving
m∠1=x+10
m∠2=3x+18
by using the given Fig.1 we get m∠1=48∘
m∠2=132∘.
Geometry Chapter 2 Exercise 2.8 Free Solutions Page 30 Problem 7 Answer
Here, we have given a figure in which we have given three angles, that are ∠3,∠4,∠5 .Further, we can say we have given
m∠3=90∘
m∠4+m∠5=90∘.
Thus we just have to find the value of m∠4,m∠5.
As we have given m∠4=2x−5……(1)
m∠5=4x−13……(2)
And from the given figure we also have m∠4+m∠5=90∘
Thus we will have
2x−5+4x−13=90∘
6x−18=90
6x=108
x=18∘
Now we will just put the value of x in eq. 1 and 2 respectively,
we will have
m∠4=2x−5
=2⋅18−5
=36−5
=31∘and
m∠5=4x−13
=4⋅18−13
=59∘
Hence by solving
m∠4=2x−5
m∠5=4x−13
by using the given Fig.1.
we get m∠4=31∘
m∠5=59∘
Geometry Homework Practice Workbook Exercise 2.8 Student Solutions Page 30 Problem 8 Answer
Here, we have given
And we have to find the unknown value of the angles m∠6 and m∠7 by using the given figure.
As we know that a theorem states that the two opposite angles are equal when two straight lines intersect, forming four angles.
So now we can write m∠6=m∠7
That implies
7x−24=5x+14
7x−5x=14+24
2x=38
x=19∘
Thus putting x in eq. 1 and 2, we will have
m∠6=7x−24
=7⋅19−24
=133−24
=109∘and
m∠7=5x+14
=5⋅19+14
=95+14
=109∘
Hence by solving m∠6=7x−24
m∠7=5x+14 by using the given Fig.1.we get m∠6=m∠7=109∘.
Inductive Reasoning And Conjecture Exercise 2.8 Geometry Workbook Answers Page 30 Problem 9 Answer
Here we have given straight lines referred to as the road names.
So as the figure says, Barton rode and Olive tree lane is making 90∘angle where Tryon street and Olive tree lane is making 57∘angle.
So as we have been told, we just need to find the acute angle made by Tryon Street with Barton Road.
As we know that
The angle between Barton Road and Olive tree lane+The angle between Barton Road and Tyron St.+
Tyron St. and Olive tree lane=180∘
⇒90∘+The angle between Barton Road and Tyron St.+57∘
⇒The angle between Barton Road and Tyron St.=180∘−90∘−57∘
=33∘
So the measure of the acute angle Tryon Street forms with Barton Road will be
= 90∘+The angle between Barton Road and Tyron St.
=90∘+33∘
=123∘
Hence by using the given Fig.1, we have measured the acute angle Tryon Street forms with Barton Road is 123∘.