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
AfilCa [17]
3 years ago
11

Examine the figure below.

Mathematics
1 answer:
Sliva [168]3 years ago
4 0

*see attachment for diagram

Answer:

✔️m<BAC = 72°

✔️m<BCD = 108°

Step-by-step explanation:

Given:

m<ABC = (4x - 16)°

m<ACB = (5x + 7)°

Find the numerical value of m<ABC, m<ACB, m<BAC, and m<BCD.

First we need to determine the value of x.

The ∆ given is an isosceles triangle with two equal sides, therefore, the angles opposite the two equal sides would also be equal.

Therefore:

(4x - 16)° + 2(5x + 7)° = 180° (sum of ∆)

Solve for x

4x - 16 + 10x + 14 = 180

Add like terms

14x - 2 = 180

Add 2 to both sides

14x = 182

Divide both sides by 14

x = 13

Find the measure of each angle by plugging in the value of x where necessary:

✔️m<ABC = (4x - 16)° = 4(13) - 16

m<ABC = 36°

✔️m<ACB = (5x + 7)° = 5(13) + 7

m<ACB = 72°

✔️m<BAC = m<ACB (both are base angles of the isosceles ∆, so they are equal)

Therefore,

m<BAC = 72°

✔️m<BCD = m<ABC + m<ACB (exterior angle theorem of a triangle)

m<BCD = 36 + 72 (Substitution)

m<BCD = 108°

Therefore, the angle measures that are correct are:

✔️m<BAC = 72°

✔️m<BCD = 108°

You might be interested in
The sum of three consecutive odd integers 171
Artyom0805 [142]
55,57,59 
Let the smallest integer = x
171= (x) + (x+2) + (x+4)
171= 3x + 6
3x = 165
x= 55
therefore the integers are 55, 57, 59
6 0
3 years ago
Coffee Tea
Lelu [443]

Answer:

A larger percentage of people in New York prefer coffee

3 0
2 years ago
Will mark Brainlest!! <br>Help Please!<br>(1). find the domain and range of the following <br>​
miss Akunina [59]

Answer:

Step-by-step explanation:

You have the domain. It is given as -1≤x≤1

Now all you have to do is figure out the range which is the y value. At first glance I think it might be 3, but that does not look very logical. I'll post this much of it now and be back in under an hour with a more complete answer.

Of course! How silly of me. There is a minimum of y = 1 in the range which comes from x = 0

I've included a graph so you can see how this all works.

So the range = 1 ≤ y ≤ 3

5 0
3 years ago
How many natural numbers are between 45 and 58?
Eddi Din [679]

Answer:

12

Step-by-step explanation:

You could actually list the numbers between (but not including) 45 and 58:

{46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57}.  I count 12 numbers here.

5 0
3 years ago
Read 2 more answers
How many quarts of pure antifreeze must be added to 8 quarts of a 40% antifreeze solution to obtain a 60% antifreeze solution
anyanavicka [17]

Let <em>q</em> be the number of quarts of pure antifreeze that needs to be added to get the desired solution.

8 quarts of 40% solution contains 0.40 × 8 = 3.2 quarts of antifreeze.

The new solution would have a total volume of 8 + <em>q</em> quarts, and it would contain a total amount of 3.2 + <em>q</em> quarts of antifreeze. You want to end up with a concentration of 60% antifreeze, which means

(3.2 + <em>q</em>) / (8 + <em>q</em>) = 0.60

Solve for <em>q</em> :

3.2 + <em>q</em> = 0.60 (8 + <em>q</em>)

3.2 + <em>q</em> = 4.8 + 0.6<em>q</em>

0.4<em>q</em> = 1.6

<em>q</em> = 4

4 0
2 years ago
Other questions:
  • In the problem what is 2×2?
    13·2 answers
  • The total cost for my brother's bowling party was \$140 sign, 140. It cost \$50$ sign, 50 to reserve a bowling lane plus the cos
    10·1 answer
  • 3y + 1 = 22 what’s the equation
    8·2 answers
  • What is the simplest form for 10/25 ?
    6·2 answers
  • If you toss a coin and spin the spinner what is the probability of heads and read? a) 1/8 b)1/4 c) 1/2 d) 3/4
    11·2 answers
  • Identify the correct trigonometry formula to use to solve for the given angle.
    9·1 answer
  • 25e + -6e_7 =<br> Whats the answer
    6·1 answer
  • A lawn sprinkler spins in a circle. The sprinkler covers a radius of 12 feet. Which choice is the closest to the area of lawn th
    7·1 answer
  • The answer to 68 + (-43) is?
    10·2 answers
  • F(x) = 2x-5<br> Complete the function table.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!