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
Find the area of this shape. Correct answer will Brainliest
Iteru [2.4K]

Answer:

As shown in picture, this is a trapezoid.

The area of a trapezoid is calculated by:

A = (base1 + base2) x height x (1/2)

To work out A, we need to find out base1, base2, and height.

base1  = YZ = \sqrt{(Zx - Yx)^{2} + (Zy - Yy)^{2} } = \sqrt{(5 - 2)^{2} + (5 - 5)^{2} } = 3

base2 = XW =\sqrt{(Wx - Xx)^{2} + (Wy - Xy)^{2} } = \sqrt{(8 - 1)^{2} + (1 - 1)^{2} } = 7

Otherwise, the height (distance between base1 and base2) is 4 as shown in picture.

=> A = (3 + 7) x 4 x (1/2) = 20

Hope this helps!

:)

6 0
3 years ago
Heeeeeeeeeeeeeeeeeeeeeeeeeeeeeeelp
Tema [17]

Answer:

1. not possible, 2. a. 65 b. 115  c.115

Step-by-step explanation:

def. sup. <

vertical angles post.

corresponding angles thm.

4 0
3 years ago
Read 2 more answers
Help me plz ASAP
Hatshy [7]
The equation has one solution
4 0
3 years ago
2) if -2(3y 5)=-4, find the value of 5y
Radda [10]
Distribute the ( ).....get -6y -10= -4 Add 10 on both sides, get -6y=6. Divide by-6, get y of -1
4 0
3 years ago
This graph represents the positions
sleet_krkn [62]

Answer:

step g

Step-by-step explanation:

it axis is giong up more than other turtle which makes more sense.

for more homework awnser follow me on instagram ad dm me.

its.emma.sloan

4 0
3 years ago
Other questions:
  • solve the following system of equations express your answers as an ordered pair in the format (a,b) with no spaces between the n
    9·2 answers
  • Solve the equation 3/4x-5=x
    6·1 answer
  • I had help but still don't understand plz help
    9·1 answer
  • The probability that a battery will last 10 hr or more is 0.9, and the probability that it will last 15 hr or more is 0.12. Give
    7·1 answer
  • A. Find m<br> b. you write the measures of
    15·1 answer
  • What are the domain and range of g(x) = -1/4 (x-17)^2 + 61?<br><br><br>​
    15·1 answer
  • True or false 33 over 3 equals 11.3? ​
    8·2 answers
  • PLEASE HELP WITH THIS I SHALL GIVE BRAINLIEST
    9·2 answers
  • What is 7 fewer than a number s
    11·1 answer
  • Which of the following is the solution to | x1-5 ≤ -13?
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!