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
meriva
3 years ago
5

If \orange{\angle ADC}∠ADCstart color #ffa500, angle, A, D, C, end color #ffa500 measures 23^\circ23 ∘ 23, degrees, what does \b

lue{\angle ABC}∠ABCstart color #6495ed, angle, A, B, C, end color #6495ed measure?
Mathematics
2 answers:
3241004551 [841]3 years ago
5 0
Can you just post the pic
igomit [66]3 years ago
4 0

Answer:

23 degrees

Step-by-step explanation:

First add a diameter. The triangle \pink{ABD}ABDstart color #ff00af, A, B, D, end color #ff00af is isosceles as \pink{AB}ABstart color #ff00af, A, B, end color #ff00af and \pink{BD}BDstart color #ff00af, B, D, end color #ff00af are radii, so must be equal. Therefore, \pink{\angle{BAD}}∠BADstart color #ff00af, angle, B, A, D, end color #ff00af and \orange{\angle{ADB}}∠ADBstart color #ffa500, angle, A, D, B, end color #ffa500 are equal. Since, the angles in a triangle sum to 180^\circ180   180∠ABD+∠BAD+∠ADB∠ABD+2⋅∠ADB∠ABD===180∘180∘180∘−2⋅∠ADB

So, \blue{\angle{ABE}} = 2 \cdot \orange{\angle{ADB}}∠ABE=2⋅∠ADBstart color #6495ed, angle, A, B, E, end color #6495ed, equals, 2, dot, start color #ffa500, angle, A, D, B, end color #ffa500. We can also create an isosceles triangle, \pink{BCD}BCDstart color #ff00af, B, C, D, end color #ff00af.Using the same argument we can find that, \blue{\angle{CBE}} = 2 \cdot \orange{\angle{CDB}}∠CBE=2⋅∠CDBstart color #6495ed, angle, C, B, E, end color #6495ed, equals, 2, dot, start color #ffa500, angle, C, D, B, end color #ffa500.∠ABC=∠ABE−∠CBEstart color #6495ed, angle, A, B, C, end color #6495ed, equals, start color #6495ed, angle, A, B, E, end color #6495ed, minus, start color #6495ed, angle, C, B, E, end color #6495ed

\orange{\angle{ADC}} = \orange{\angle{ADE}} - \orange{\angle{CDE}}∠ADC=∠ADE−∠CDEstart color #ffa500, angle, A, D, C, end color #ffa500, equals, start color #ffa500, angle, A, D, E, end color #ffa500, minus, start color #ffa500, angle, C, D, E, end color #ffa500

Hint #1010 / 11

Since \blue{\angle{ABE}} = 2 \cdot \orange{\angle{ADE}}∠ABE=2⋅∠ADEstart color #6495ed, angle, A, B, E, end color #6495ed, equals, 2, dot, start color #ffa500, angle, A, D, E, end color #ffa500 and \blue{\angle{CBE}} = 2 \cdot \orange{\angle{CDE}}∠CBE=2⋅∠CDEstart color #6495ed, angle, C, B, E, end color #6495ed, equals, 2, dot, start color #ffa500, angle, C, D, E, end color #ffa500, \blue{\angle{ABC}} = 2 \cdot \orange{\angle{ADC}}∠ABC=2⋅∠ADCstart color #6495ed, angle, A, B, C, end color #6495ed, equals, 2, dot, start color #ffa500, angle, A, D, C, end color #ffa500

Hint #1111 / 11

So, \orange{\angle{ADC}} = \frac{1}{2} \cdot \blue{46^\circ} = 23^\circ∠ADC=  

2

1

​  

⋅46  

∘

=23  

∘

start color #ffa500, angle, A, D, C, end color #ffa500, equals, start fraction, 1, divided by, 2, end fraction, dot, start color #6495ed, 46, degrees, end color #6495ed, equals, 23, degrees

You might be interested in
Which expressions represent this model?
Alenkasestr [34]
The expressions that represent this model is 4(5), 5(4), and 20
3 0
3 years ago
Read 2 more answers
Match the numbers in standard notation with the corresponding numbers in scientific notation.
ankoles [38]

Answer:

a) 864,000,000,000      8.64E11

b) 8,640,000,000           8.64E9

c) 86,400,000,000,000     8.64E13

d) 864,000,000,000,000    8.64E14

Step-by-step explanation:

A scientific notation is a way to represent very large values into the decimal form.

Steps to write in scientific notation:

Move the decimal to left before first digit of the given number.

Find the number of times decimal is moved to left.

Put that number in the exponent of e.

So, matching:

a) 864,000,000,000      8.64E11

b) 8,640,000,000           8.64E9

c) 86,400,000,000,000     8.64E13

d) 864,000,000,000,000    8.64E14

8 0
3 years ago
Need answer for this
anastassius [24]
11 kilometers! hope that helped
6 0
2 years ago
Take west to be the positive direction. The height of a sloped roof above the place where you stand is 12
den301095 [7]

<u>Given:</u>

Take west to be the positive direction. The height of a sloped roof above the place where you stand is 12  feet. If you move 3 feet west, the height is 10 feet.

We need to determine the slope.

Let x denote the standing place.

Let y denote the height.

Writing the given as coordinates, we get;

(0,12) and (3,10)

<u>Slope</u>:

The slope can be determined using the formula,

m=\frac{y_2-y_1}{x_2-x_1}

Substituting the coordinates (0,12) and (3,10), we have;

m=\frac{10-12}{3-0}

m=\frac{-2}{3}

Thus, the slope is m=-\frac{2}{3}

7 0
3 years ago
Refer to matrix A and identify the matrix element a31.
Blizzard [7]
<h3>Answer:  D) 7</h3>

===================================================

Explanation:

a31 means "the value in the third row, first column". That value is 7

As another example, a22 = 3 since 3 is in the second row, second column.

Another example: a12 = -1 because we're in the first row and second column.

This is a 3x2 matrix due to it having 3 rows and 2 columns.

5 0
3 years ago
Other questions:
  • A company manufactures televisions in batches of 25 and there is a 1% rate of defects. Find the standard deviation for the numbe
    13·2 answers
  • A polygon has coordinates A(-7, 8), B(-4, 6), C(-4, 3), D(-8, 3), and E(-9, 6). What are the coordinates of its image, polygon A
    14·1 answer
  • 1y-6x=-3 <br><br> What is the answer?
    6·2 answers
  • Directions : find the area of each figure . round to the nearest tenth if necessary.
    12·2 answers
  • Two six-sided dice are rolled. Find the probability that the sum of the two faces that turn up is between 1 and 14.
    12·1 answer
  • Which equation represents a line that passes through (4.) and has a slope of
    15·1 answer
  • Joseph says that the product of a four digit number and a 1 digit number is always a four digit number does Joe didn't make sens
    11·1 answer
  • If january 1st was on a tuesday, on what day of the week would february 1 fall?
    11·2 answers
  • What’s 384.94 + 17.348
    9·2 answers
  • Choose the correct answer to 97 ÷ 4.<br> 24 R1<br> 24<br> 23 R5<br> 24 R3
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!