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
vichka [17]
3 years ago
9

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is four times

the measure of the first angle. The third angle is 12 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Mathematics
1 answer:
prohojiy [21]3 years ago
3 0

Answer:

{36, 66, 78}

Step-by-step explanation:

Let the measures of the three angles be f, s and t, for first, second and third.  Then s + t = 4f, t = 12 + s, and f + s + t = 180.

Subbing 12 + s for t in the first equation, we get s + 12 + s = 4f.

Subbing the same in the third equation, we get f + s + 12 + s = 180

This results in two equations in two unknowns (f and s):

2s - 4f = -12

2s  + f  = 168.

Let's eliminate s by subtracting the first of these two equations from the second.  Doing so yields 5f = 180.  Then the first angle, f, or x, is 36.

Then, from 2s + f = 168, we get 2s + 36 = 168, or 2s = 132.  Thus, the second angle is s = y = 66.

The sum of the three angles must be 180.  Thus, 36 + 66 + t = 180, or

102 + t = 180, or t = z = 78.

The three angles are

{36, 66, 78}.

You might be interested in
The root mean square velocity of one mole of a monoatomic gas having molar mass M is U rms . The relation between average kineti
garik1379 [7]

root means square velocity of one mole of a monoatomic gas having molar mas*s m(M) is Urms. The relation between average kinetic energy (e)of the gas and Urms is Urms=M2E

StarrySoul please check it...

8 0
2 years ago
Sophia is saving money for a new bicycle. The bicycle will cost at least $623. Sophia makes $8.22 per hour.
Luda [366]
$8.22h greater than or equal to $623
3 0
3 years ago
Read 2 more answers
I will name you the brainliest ! Which point represents -(-10) on the number line?
Anna007 [38]

Answer:

e

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Please solve the equation _4(4n+2)=4
MrRissso [65]
16n+8=4
16n=4-8
16n=-4
n=-4/16
n=-1/4.
8 0
3 years ago
Read 2 more answers
Barb earns 26% commission on each lab manual she sells. If she sells 1200 manuals at $9.95 each, find her commission.
kvasek [131]
1200 × 9.95 = 11.940 × 26 =310,440 ÷ 100 = 3,104.40 her commission is $ 3,104.40
6 0
3 years ago
Other questions:
  • List all the factors of 33
    10·1 answer
  • What is the sum of 4 8/10 and 1 1/2
    11·2 answers
  • HELP PLEASE!
    13·1 answer
  • Multiple (7s^5)(-1/5s^3​
    15·1 answer
  • What is the equation for 5(x+2)=40
    15·2 answers
  • Simplify a-c when a=5,c=-1​
    5·1 answer
  • Will x + 1/2 = x - 1/2 be always true or never true?
    9·2 answers
  • Plz Solve Will Mark Brainliest and No Stealing Points Or Will Report<br> Part 1
    8·1 answer
  • Find the surface area of the triangular prism shown below.
    9·1 answer
  • Select the statment that correctly describes the solution to this system of equations.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!