Question

For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)° , what is the measure of each angle?(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

Vertical angles are a pair of non-adjacent angles formed by the intersection of two lines. They are always congruent, which means they have the same measure.

Therefore, we can set up an equation and solve for x to find the measure of each angle:

m∠2 = m∠4

(5x + 23)° = (3x + 35)°

Simplifying the equation:

5x + 23 = 3x + 35

Subtracting 3x from both sides:

2x + 23 = 35

Subtracting 23 from both sides:

2x = 12

Dividing both sides by 2:

x = 6

Now we can substitute x = 6 back into the original equations to find the measure of each angle:

m∠2 = 5x + 23 = 5(6) + 23 = 30 + 23 = 53°

m∠4 = 3x + 35 = 3(6) + 35 = 18 + 35 = 53°

Therefore, the measure of each angle is 53°.

Answer 2

Two angles make a vertical pair: m∠1=(3x+15)°

and m∠3=(x+45)°
. What is the measure of each angle?

Answer 3

[AI-generated answer — Bot GPT 3.5]

Since angles 1 and 3 form a vertical pair, they are congruent.

Therefore, we can set up an equation and solve for x to find the measure of each angle:

m∠1 = m∠3

(3x + 15)° = (x + 45)°

Simplifying the equation:

3x + 15 = x + 45

Subtracting x from both sides:

2x + 15 = 45

Subtracting 15 from both sides:

2x = 30

Dividing both sides by 2:

x = 15

Now we can substitute x = 15 back into the original equations to find the measure of each angle:

m∠1 = 3x + 15 = 3(15) + 15 = 45 + 15 = 60°

m∠3 = x + 45 = 15 + 45 = 60°

Therefore, the measure of each angle is 60°.