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3 years ago

Angle ABC is inscribed in a circle as shown.What is the measure, in degrees, of angle ABC?

Mathematics

1 answer:

sladkih [1.3K]3 years ago

5 0

Answer

Find out the measure, in degrees, of angle ABC .

To prove

The relationship between inscribed angles and their arcs

The measure of an inscribed angle is half the measure the intercepted arc.

The formula is

$Measure\ of\ inscribed\ angle = \frac{1}{2}\times measure\ of\ intercepted\ arc$

As given in the diagram

The measure of the intercepted arc A to B is 120°.

Put value in the formula

$\angle ABC = \frac{1\times 120^{\circ}}{2}$

∠ABC = 60°

Therefore the measure of the ∠ABC is 60° .

You might be interested in

Is the relation a function?<br><br> Select Yes or No for each relation.

Lina20 [59]

Hello! There are a few things that determine whether or not something is a function. In this case, to determine whether a relation is a function, we look at the domains, which are the x-coordinates, the first number of the pair. If the number occurs in the x-coordinate for more than one pair in a relation, then it's not a function. If a number only occurs as an x-coordinate once in the relation, then it's a function. In other words, they each have only one y-coordinate in the relation. For this question, the first, second, and third relations are functions. The fourth one is not a function, because the 3 has more than one y-coordinate, so it occurs as an x-coordinate more than once. Here are the answers easier to read.

1st : yes
2nd: yes
3rd: yes
4th: no

3 0

3 years ago

Which of the following systems of inequalities has point D as a solution? Two linear functions f of x equals 3 times x plus 4 an

Pani-rosa [81]

Answer:

B) f(x) ≥ 3x + 4

g of x is less than or equal to negative one half times x minus 5

Step-by-step explanation:

From the above graph,

If point B is the solution of the system of inequalities, then point B must satisfies both inequalities

We can see from the graph that

Point B is located above (≥) the boundary line for f(x) and is also below (≤) the boundary line for g(x).

So we can say,

Point b satisfies the inequalities

Therefore,

The system is

f(x) ≥ (3x+4)

g(x) ≤ (-1/2x -5)

Hopes this Helps :)

8 0

3 years ago

a line passes through point (-2,5) and has a slope of 2/3 points a (x,3) and b ( -2, y) lie on the line what is the value of y a

Tomtit [17]

Answer:

The value of y is 5 , and The value of x is - 5

Step-by-step explanation:

Given as :

The line passes through point ( - 2, 5)

The slope of line is m = $\frac{2}{3}$

Equation of line is written as

y - $y_1$ = m × (x - $x_1$ )

Since line passes through line ( - 2 , 5 ) and have slope $\frac{2}{3}$

So, y - 5 = $\frac{2}{3}$ × (x + 2)

Or, 3 × ( y - 5 ) = 2 × ( x + 2 )

Or, 3 y - 15 = 2 x + 4

Or, 3 y - 2 x - 19 = 0 is the equation of line

Now points ( x , 3 ) lies on the line 3 y - 2 x - 19 = 0

So, 3 × 3 - 2 x - 19 = 0

or, 9 - 2 x - 19 = 0

or, 2 x = - 10

∴ x = - $\frac{10}{2}$

I.e x = - 5

Again points ( - 2 , y ) lies on the line 3 y - 2 x - 19 = 0

So, 3 × y + 2 × 2 - 19 = 0

Or, 3 × y + 4 -19 = 0

or, 3 y = 15

∴ y = $\frac{15}{3}$

I.e y = 5

Hence The value of y is 5 , and The value of x is - 5 . Answer

8 0

2 years ago

Write the standard form of the equation:<br> Slope= 3 y-intercept= -1

Amiraneli [1.4K]

Answer:

y=3x-1

Step-by-step explanation:

y=mx+b

y=3x+b

y=3x-1

7 0

2 years ago

Identify each sequence as arithmetic or geometric. Explain your answer, and write an explicit formula for the

NeX [460]

Answer:

Geometric Sequence

Step-by-step explanation:

In this case it is Geometric Sequence as it has a common ratio of 5

Formula for nth term: a(n) = ar∧n-1

so if we take the third term we will calculate as follows:

50 = 2(r)∧3-1

50÷2 = r∧2

√25= r

r=5

7 0

3 years ago