The measure of an exterior angle of a triangle is equal to which of the following measures?

The measure of its complementary angle
The measure of its adjacent angle
The sum of the measures of the interior angles
The sum of the measures of its remote interior angles

The sum of the measures of its remote interior angles

Step-by-step explanation:

Let the triangle be ABC with their angles AB BC CA and

angle a, b and c.

We know that sum of angles of triangle is 180

so a + b + c = 180

=> a = 180 - (b + c)    equation 1

Now lets find the value for exterior angle of angle a.

we know that sum of angle on straight line 180 degree

as angle a and its exterior angle lie on straight line

therefore => angle a +  exterior angle a = 180

=> exterior angle a = 180 - a

substituting value angle a from equation 1

exterior angle a = 180 - (180 - (b + c))

=> exterior angle a =  b + c ( angle b and angle c are remote exterior angle to exterior angle a)

similarly we can perform above steps to find exterior angle b and exterior angle c which will be sum of  measures of its respective remote interior angles

Thus we see that value of exterior angle is sum of measure of its remote interior angles

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square