1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mart [117]
3 years ago
7

In the figure above line m is parallel to line n.

Mathematics
1 answer:
enot [183]3 years ago
7 0

<u>Given</u>:

Line m is parallel to line n.

The measure of ∠1 is (4x + 15)°

The measure of ∠2 is (9x + 35)°

We need to determine the measure of ∠1

<u>Value of x:</u>

From the figure, it is obvious that ∠1 and ∠2 are linear pairs.

Thus, we have;

\angle 1+\angle 2=180^{\circ}

Substituting the measures of ∠1 and ∠2, we get;

4x+15+9x+35=180

             13x+50=180

                     13x=130

                        x=10

Thus, the value of x is 10.

<u>Measure of ∠1:</u>

The measure of ∠1 can be determined by substituting x = 10 in the measure of ∠1

Thus, we have;

\angle 1 =4(10)+15

    =40+15

\angle 1=55^{\circ}

Thus, the measure of ∠1 is 55°

You might be interested in
Find the value of the variable.
nalin [4]

Answer:

The variable, y is 11°

Step-by-step explanation:

The given parameters are;

in triangle ΔABC;          {}              in triangle ΔFGH;

Segment \overline {AB} = 14         {}               Segment \overline {FG} = 14

Segment \overline {BC} = 27         {}              Segment \overline {GH} = 19

Segment \overline {AC} = 19         {}               Segment \overline {FH} = 2·y + 5

∡A = 32°                       {}                ∡G = 32°

∡A = ∠BAC which is the angle formed by segments \overline {AB} = 14 and \overline {AC} = 19

Therefore, segment \overline {BC} = 27, is the segment opposite to ∡A = 32°

Similarly, ∡G = ∠FGH which is the angle formed by segments \overline {FG} = 14 and \overline {GH} = 19

Therefore, segment \overline {FH} = 2·y + 5, is the segment opposite to ∡A = 32° and triangle ΔABC ≅ ΔFGH by Side-Angle-Side congruency rule which gives;

\overline {FH} ≅ \overline {BC} by Congruent Parts of Congruent Triangles are Congruent (CPCTC)

∴ \overline {FH} = \overline {BC} = 27° y definition of congruency

\overline {FH} = 2·y + 5 = 27° by transitive property

∴ 2·y + 5 = 27°

2·y = 27° - 5° = 22°

y = 22°/2 = 11°

The variable, y = 11°

8 0
2 years ago
The height of a cone-shaped statue is 9 ft, and the diameter is 12 ft.
Pepsi [2]
I hope this helps you



Volume of cone =1/3.pi.r^2.h



Volume of cone =1/3.3,14.6^2.9



Volume of cone =339.12
3 0
3 years ago
Read 2 more answers
Suppose two $20 bills, three $10 bills, one $5 bill, and seven $1 bills are placed in a bag. If you were to pull a bill at rando
Korolek [52]

Answer:

Assuming that the $1 bill was pulled at random, then the expected value of the amount chosen is \frac{7}{13}.

Step-by-step explanation:

From the given question, the bag contains;

$1 bill = 7

$5 bill = 1

$10 bill = 3

$20 bill = 2

Total number of bills in the bag = 13

Pulling a bill at random, the bills would have an expected value as follows:

For $1 bill, the expected value = \frac{7}{13}

For $5 bill, expected value = \frac{1}{13}

For $10 bill, expected value = \frac{3}{13}

For $20 bill, the expected value = \frac{2}{13}

Assuming that the $1 bill was pulled at random, then the expected value of the amount chosen is \frac{7}{13}.

6 0
3 years ago
What is equivalent to the product of nine and b cubed
ankoles [38]
The expression is
9b^3
5 0
3 years ago
What is the answer to 2/3j-1/6=1/2?
Elodia [21]
It has already given you the answer.
3 0
3 years ago
Other questions:
  • There is a cafe at the carpark it is 13 metres long and 8 metres wide what is the area of the cafe
    7·2 answers
  • What is the surface area of the right cone below?
    13·1 answer
  • How many people can you serve with 6 pizzas if each pizza is 3/4 of a pizza?
    14·1 answer
  • Explain why estimation is an important skill to know when adding and subtracting decimals.
    8·2 answers
  • A punch recipe requires 2 cups of cranberry juice to make 3 gallons of punch. Using the same recipe, what is the amount of cranb
    11·1 answer
  • Find the 11th term of the following geometric sequence.<br> 2, 8, 32, 128, ...
    13·1 answer
  • PLEASE HELP!!!!
    15·1 answer
  • Yuugffghhgfffrrrreddddfffifufu​
    11·2 answers
  • Given the function f(3) = 36 complete the following table​
    6·1 answer
  • How do you find what exponents of i are? like I know i^2 is -1, but how are you supposed to figure out i^26? do you have to writ
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!