All categories

3 years ago

The measure of ∠DAB equals 105º. The measure of ∠ACB equals 35º.What is m∠ABC?

Mathematics

2 answers:

Leni [432]3 years ago

8 0

1) We know that <DAB and <BAC are supplementary angles according to the exterior angle theorem, so we set up the following equation and solve:

105+x=180

x=75

2) Since we have the angles for <BAC and <ABC and a triangle has its total angles added up to 180, we can set up an equation to find <ABC and solve:

75+35+x=180

110+x=180

x=70

So the m<ABC is 70 degrees.

Hope this helped! Let me know if you need me to clarify anything.

Deffense [45]3 years ago

4 0

Answer: Angle ABC is 70 degrees.

Step-by-step explanation:

We know that angle ACB is 35 degrees. We can also see in the picture that angle DAB and angle CAB are supplementary angles. Supplementary angles are 180 degrees so you can find CAB by subtracting 180 by 105(angle DAB is 105 degrees). So, CAB is 75 degrees. A triangle angles are always 180 degrees, so you can simply add angle CAB(75 degrees) and angle ACB(35 degrees), and subtract 180 from it:

35+75+?=180. ?= angle ABC

110+?=180

110-110+?=180-110

?=70

You might be interested in

The midpoint of \overline{\text{AB}} AB is M(-3, -3)M(−3,−3). If the coordinates of AA are (-5, -1)(−5,−1), what are the coordin

astraxan [27]

The coordinates of point B are (-1,-5)

Step-by-step explanation:

The formula for mid-point is given by:

$M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})$

Given

M(x,y) = (-3,-3)

A(x1,y1) = (-5, -1)

We have to find the coordinates of B(x2,y2)

So,

$M(x,y)= (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\(-3,-3) = (\frac{-5+x_2}{2} , \frac{-1+y_2}{2})\\putting\ respective\ coordinates\ equal\\-3 = \frac{-5+x_2}{2}\\-3 * 2 = -5+x_2\\-6 = -5+x_2\\-6+5 = x_2\\x_2 = -1\\And\\-3 = \frac{-1+y_2}{2}\\-3*2 = -1+y_2\\-6 = -1+y_2\\-6+1 = y_2\\y_2 = -5$

Hence,

The coordinates of point B are (-1,-5)

Keywords: Mid-point, coordinates

Learn more about mid-point at:

#LearnwithBrainly

5 0

3 years ago

Suppose you have 12 coins that total 32 cents . Some of the coins are nickels and the rest are pennies . How many of each coin d

mario62 [17]

You will need 6 coins of 5
and 2 coins of 1
hope it helps

=) = )

8 0

3 years ago

Find the value of x. F 8 E Х Н. Х -

Vladimir79 [104]

Answer:

Step-by-step explanation:

x = 8

3 0

3 years ago

The third term of an arithmetic sequence is 21, and the eighth term is 56. The first term is _____.

aleksley [76]

The first term is 7. This is because the sequence has a pattern of increasing by 7. If the first term was 7, the second would be 14, the third would be 21. The 4th would be 28, continue to the 8th term 56.

5 0

3 years ago

A $20, 000 brand new car depreciate its value every year following the pattern, $16,000, $12,800, $10,240. How much will the car

seropon [69]

Answer:

Step-by-step explanation:

Use the info given in the exponential equation to find the value of b, the rate of decay.

$v(t)=a(b)^t$ where v(t) is the value of the car after a certain number of years, t, have gone by, a is the initial value, and b is the rate of decay. We have everything we need but b:

a = 20000

v(t) = 16000 after t = 1 year:

$16000=20000(b)^1$ so

b = .8 Taken in context, this means that the car depreciates 20% each year. Now we can solve the problem being asked of us, which is to find the value of the car after t = 5 years:

$v(t)=20000(.8)^5$ which simplifies down a bit to

v(t) = 20000(.32768) so

v(t) = 6553.60, choice C.

7 0

3 years ago