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
aliya0001 [1]
2 years ago
5

What is the measure (in degrees) of the smallest interior angle of a triangle in which the exterior angle measures have the rati

o $3:4:5$?
Mathematics
2 answers:
steposvetlana [31]2 years ago
8 0

Let

3x----> angle exterior 1

4x----> angle exterior 2

5x----> angle exterior 3


we know that

The exterior angles of any polygon add up to 360 degrees

so

3x+4x+5x=360-------> 12x=360----------> x=30°


The largest of exterior angles is equal to the smallest of interior angles

so

the largest of exterior angles is 5x------> 5*30=150°

the smallest of interior angles is 180°-150°=30°


therefore


the answer is

the smallest of interior angle measure 30 degrees

SVEN [57.7K]2 years ago
6 0

Answer:

30 degrees

Step-by-step explanation:

Since the exterior angle measures have the ratio $3:4:5$, they are $3x:4x:5x$ for some value of $x$. Each exterior angle is supplementary to an interior angle, so the measures of the interior angles of the triangles are $180^\circ - 3x$, $180^\circ - 4x$, and $180^\circ - 5x$. The sum of the interior angles of a triangle equals $180^\circ$, so we have

\[(180^\circ -3x) + (180^\circ - 4x) + (180^\circ - 5x) = 180^\circ.\]Simplifying this equation gives $-12x = -360^\circ$, so $x = 30^\circ$. Therefore, the smallest interior angle has measure $180^\circ - 5x = \boxed{30^\circ}$.

You might be interested in
Given the following system of equations:
Artemon [7]

Answer: Divide the first equation, −4x + 8y = 16, by 2

Step-by-step explanation:

3 0
3 years ago
Find the equation of the line.
Ymorist [56]

Answer:

y = 0,5 x + (-3)

Step-by-step explanation:

We can see from the graph that when y = -3, the line crosses y axis, therefore

y = ? x + (-3)

We can also spot that when x = 6, y = 0

// now mark ? sign as a variable k and put the given x and y values into the previous expression

y = k * x - 3

0 = k * 6 - 3

k * 6 = 3

k = 3/6

k = 0,5

3 0
2 years ago
If y varies inversely as x and y=3 when x=4, then y=12 when x=15 <br><br> True or false ?
Elden [556K]

y=12 is false answer.

8 0
3 years ago
What is 3x²+5x+25 when x equals 3
Ksivusya [100]

Answer: 67

Step-by-step explanation:

3x^2 + 5x + 25

x = 3

3(3)^2 + 5(3) + 25

3^2 = 9

3(9) + 5(3) + 25

3 * 9 = 27

27 + 5(3) + 25

5 * 3 = 15

27 + 15 + 25

27 + 15 = 42

42 + 25 = 67

8 0
3 years ago
Read 2 more answers
Oscar bought 15 gallons of water at $1.98 per gallon. He wants to divide this water in bottles of 1/8 gallon each. What is the c
Licemer1 [7]

Answer:

Step-by-step explanation:

8 0
2 years ago
Other questions:
  • Help please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11
    15·1 answer
  • What is the area of this trapezoid?<br><br><br><br><br> Enter your answer in the box.
    14·1 answer
  • Is the supplement of an acute angle is an obtuse angle
    14·2 answers
  • Plants are set up in a greenhouse. 1/3 of potted plants are grown under red light, 1/3 under green light, and 1/3 under natural
    9·2 answers
  • Which of the following expressions does not mean the same as the other three?
    8·2 answers
  • Which is the least time 9.675,9.7,9.75
    11·1 answer
  • Which statement is true about the expression 7(2x 5)A. The expression has two factorsB. The expression has three factors.C. The
    12·1 answer
  • Let a=(1,2,3,4), b=(4,3,2,1) and c=(1,1,1,1) be vectors in R4. Part (a) [4 points]: Find (a⋅2c)b+||−3c||a. Part (b) [6 points]:
    15·1 answer
  • Help please due in a hour
    15·1 answer
  • Plssss i need help<br><br><br><br><br>ASAPP​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!