If the measure of the third angle of the triangle is 45 ​° more than three time the measure of either of the other two​ angles, find the measure of each angle of the triangle.​ (Recall that the sum of the measures of the angles of a triangle is​ 180°.)

Answers

Answer 1

Answer:

The first and second angles are 27° and the third angle is 126°.

Step-by-step explanation:

We have that the third angle (β) is 45° more than three times the measure of either of the other two​ angles (θ):

[tex] \beta = 45 + 3\theta [/tex]     (1)

Also, the sum of the measures of the 3 angles is 180°:

[tex] \beta + \theta + \theta = 180 ^{\circ} [/tex]   (2)

By entering equation (1) into equation (2) we have:

[tex] 45 + 3\theta + \theta + \theta = 180 [/tex]  

[tex] 5\theta = 180 - 45 [/tex]

[tex] \theta = 27 [/tex]

Hence, the third angle is:

[tex] \beta = 45 + 3\theta = 45 + 3*27 = 126 [/tex]                                  

Therefore, the first and second angles are 27° and the third angle is 126°.

I hope it helps you!


Related Questions

Please answer! Thank you so so much and you will be rewarded in points!!
If the line passes through (-4,-7) and (4,9), what is the equation of the line in standard form?


2x - y = 1
2x + y = -1
2x + y = 1
2x - y = -1

Answers

Answer:

Step-by-step explanation:

Y=2x+1??

Answer:

2x - y = -1

Step-by-step explanation:

hope this helps

What is the average rate of change in height over the entire 5 seconds?

Answers

Answer:“To get the average rate of change between 2 points...” To get the average rate of change between 2 points, plug in their coordinate values into the equation (y2-y1)/(x2-x1). The values come from the points (x1,y1) and (x2,y2).

Step-by-step explanation:

Numbers like 10, 100, 1,000, and so on are called

Answers

Answer:

Powers of ten

Step-by-step explanation:

They are the result of multiplying 1= times iteself however many times.  

4/-7 + -6/5

In simplest form​

Answers

See attachment for math work and answer.

ft. = 4.8 yd.
How many feet is it

Answers

The answer is 14.4 feet

Answer this problem
-3+(-2)​

Answers

Answer:

-5

Explaination:

Because -3-2 is -5.

The answer is -5, because you are adding two negatives, the sign stays the same.

can u guys help with my one question i have left

Answers

Answer:

Weeks in a Year. A normal year has 365 days, which is 52 Weeks and 1 Day. A leap year has 366 days, which is 52 .

Step-by-step explanation:

hope this helps :)

Answer:

I think 6

Step-by-step explanation:

365/12=30.42

30.42/5= 6.08

What is the inverse of multiplication?

Answers

Answer:

i would say division

Step-by-step explanation:

Answer:

Division

Step-by-step explanation:

When we multiply a number is by its (multiplicative) inverse, the result is always 1. Which means, when we add any number to zero, both the operation and inverse operation will give the same number.

Mike’s fitness center charges $30 per month for a membership. All Day fitness center charges $22 per month plus an $80 initiation fee for membership. After how many months will the total amount paid to the two memberships be the same?

Answers

Answer:

10 months

Step-by-step explanation:

30x = 22x + 80

8x = 80

x = 10

the value of y varies directly with x when y=24, x=2 . what is the value of y when x is 7?

Answers

Answer:

84

Step-by-step explanation:

y∞x

y=kx (where k is the constant)

24=2k

24/2=k

12=k

therefore the relationship between k,y and x is y=12x

y=12×7

y=84

The function f(x) represents the amount of people it takes to build x engines in a car factory. What is a reasonable domain for the function f(x)?

Answers

The domain is all x-values of coordinate pairs.
But, if you need a reasonable domain for a graph, it should be all integers (whole numbers) greater than or equal to zero.
This is because you can’t have 1/2 of a person or 1/2 of an engine. You also can’t have any negative engines either. Therefore, the domain would need to be whole numbers greater than (or equal to 0).

I need help with this from start to finish


Answers

Answer:

i think you need to find the squar rout and you can just do that with a caulator.

Step-by-step explanation:

If 25% of the students in Pre-Algebra courses receive a grade of A, and there are 300 students enrolled in Pre-Algebra this year, how many students will receive an A? *

125
67
57
75

Answers

Answer:

75 students

Step-by-step explanation:

300/4

Answer:

75

Step-by-step explanation:

: Susan works as a hostess where she makes $8.75 per hour. She also babysits and earns $10.00 per hour. Last week she made $165.00. If she worked 6 hours more as a hostess than she did babysitting, how many hours did she babysit last week?

Answers

Answer:

She worked 12 hours as a babysitter and hours 6 as a hostess

Step-by-step explanation:

She woks 6 hours and gets 52.20 as a hostess so if she worked 6 hours as a babysitter then she would make 60 and 165-60=105 and since she worked 6 hours as a baby sitter than she has to work 12 hours as a hostess to make 105  we know that 105+60 =165. Forgive me if I'm wrong but I hope this helps! [creds: cosmicredstone1]

Willy Wonka has 2 candies, Wonka bars and Everlasting Gobstoppers. Both have both natural sugar and sucrose in them. Each Wonka Bar has 4 grams of natural sugar and 1 gram of sucrose. Each Everlasting Gobstopper has 2 grams of natural sugar and 3 grams of sucrose. Mr. Wonka has 60 grams of natural sugar and 75 grams of sucrose. If each Everlasting Gobstopper has a profit of $1.3 and each Wonka Bar has a profit of $3.2, how many of each candy would give him the maximum profit?

Answers

Answer:

Wonka bars=3 and  Everlasting Gobstoppers=24

Step-by-step explanation:

let the wonka bars be X

and everlasting gobstoppers be Y

the objective is to

maximize 1.3x+3.2y=P

subject to constraints

natural sugar

4x+2y=60------1

sucrose

x+3y=75---------2

x>0, y>0

solving 1 and 2 simultaneously we have

4x+2y=60----1

x+3y=75------2

multiply equation 2 by 4 and equation 1 by 1 to eliminate x we have

 4x+2y=60

 4x+12y=300

-0-10y=-240

10y=240

y=240/10

y=24

put y=24 in equation 2 we have'

x+3y=75

x+3(24)=75

x+72=75

x=75-72

x=3

put x=3 and y=24 in the objective function we have

maximize 1.3x+3.2y=P

1.3(3)+3.2(24)=P

3.9+76.8=P

80.7=P

P=$80.9

Answer:

wonka bars=3 and  Everlasting Gobstoppers=24

Step-by-step explanation:

True or false a function can sometimes be a relation ?

Answers

Answer:

Step-by-step explanation:

True

If using the vertical line test, you can tell whether something is a relation or not. If a vertical line crosses all points once it’s a function if it does not then it’s not a relation.

help me it's my homework​

Answers

Answer:

2. Answer is 4 and for 3. P= 1/4s

Step-by-step explanation:

Simply divide the values of one another.

This results you with:

8/2 = 4

12/3 = 4

10/5 = 2 -> I think there was an error or typo here

40/10 = 4

The constant proportion would be 4 because it is constant in every situation for S and P.

The equation would be p= 1/4s because 1 value of p would equal 4 s.

Help me with this question plz!!!
2x - 4=x+6

Answers

Answer:

x = 10

Step-by-step explanation:

2x - 4 = x + 6           add 4 to both sides

2x - 4 + 4 = x + 6 + 4

2x = x + 10     subtract x from both sides

2x - x = x - x + 10

x = 10

Select all sets to which the value belongs

√2- √2

Real Numbers/Irrational numbers/ Rational numbers/ Integers/Whole numbers/ Natural numbers.

Answers

Answer:

[tex] \sqrt{2} - \sqrt{2} = 0[/tex]

0 is real number, rational number, integers, whole numbers,

A small cab carries 4 people. How many small cabs will I need to transport 44 people?

Answers

44/4 = 11, so 11 small cabs would be needed to transport 44 people.
11 small cabs would be needed

Please answer these questions! Legit answers only!

Answers

Answer:

204.4 amu

Step-by-step explanation:

0.30 * 203 = 60.9

0.70 * 205 = 143.5

60.9 + 143.5 = 204.4 amu

I hope this helps!

What is the area of a
parallelogram with a base
of 2.5 cm and a height of
6 cm?

Answers

2.5 multiplied by 6 = 15

15 square centimeters

which fraction is less 2/10 or 5/8 or neither they are equal

Answers

2/10 is less, because with a common denominator they are 8/40 and 25/40.  Since 5/8 = 25/40, and 8/40 is smaller than that, 2/10 is smaller.

Answer:

2/10 is less than 5/8

Step-by-step explanation:

2/10 =0.20

5/8= 0.625

0.20<0.625

How many 1/3 cup servings are in a 12-cup container of juice?

Answers

Answer:4

Step-by-step explanation:i guess because 4 time 3 if im wrong then 1b time s 12

[(2r^2t)^3/4t^2]^2 simply

Answers

Answer:

=4r12t10

Step-by-step explanation:

Corliss earns an hourly wage, as well as tips, each day he works. His daily earned income, m, after h hours can be represented by the inequality m>11h+35.

He makes at most $11 per hour plus $35 in tips.
He makes more than $11 per hour plus $35 in tips.
He makes at least $11 per hour plus $35 in tips.
He makes less than $11 per hour plus $35 in tips.

Answers

Answer:

He makes more than $11 per hour plus $35 in tips

Step-by-step explanation:

First, you should always look at the sign and identify whether it's greater than, less than, greater than or equal to, or less than or equal to. In this inequality, the sign being shown is greater than: represented by m>11h+3

Here are inequality key words to help better understand the signs:

> : Greater Than, More Than

≥ : More Than or Equal To, At Least, No Less Than, A Minimum of

< : Less Than, Fewer Than

≤ : Less Than or Equal To, At Most, No More Than, A Maximum of

Compare v5 and 2.9.
Help :c

Answers

Answer:

√5 < 2.9

Step-by-step explanation:

√5 is 2.236...

which is less than 2.9

PLEASE HELP THANK YOU

Answers

1st one length preserved 2nd length preserved 3rd length preserved and 4th length not preserved.

Hope this helps. :D

help me plzzzzzzzzzzz

Answers

1. √8, π, 4
2. 5, π+ 2, 17/3,
3. -2, √2 , 1.7
4. 3/2, √5, 2.5
5. √13, 3.7, π + 1
6. √5/2, π - 2, 5/4

Apologies if I got some wrong

I'LL GIVE BRAINLIEST IF YOU ANSWER PLEASE I'M BEGGING

Answers

Answer:

A.

Step-by-step explanation:

Answer:

The answer is a.

Step-by-step explanation:

When you plug in 2 for n, 2 - 1  1, so we put 5 for a (because a superscript 1 = 5) and evaluate. This number then become a superscript 2.

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