For two vertical angles with measure m 2 =(5×+23)°and m4=(3×+35)°what is the measure of each angle

Answer 1

Vertical angles are formed by the intersection of two lines. They are always congruent, meaning that they have the same measure.

In this case, we have m2 = (5x + 23)° and m4 = (3x + 35)°.

Since vertical angles are congruent, we can set up the following equation:

(5x + 23)° = (3x + 35)°

To solve for x, we can start by subtracting 3x from both sides of the equation:

(5x + 23)° - (3x + 35)° = 0

(5x - 3x) + (23 - 35)° = 0

2x - 12° = 0

Next, we can add 12° to both sides of the equation:

2x - 12° + 12° = 0 + 12°

2x = 12°

Now, we can solve for x by dividing both sides of the equation by 2:

2x/2 = 12°/2

x = 6°

So, x = 6°.

To find the measure of each angle, we can substitute this value of x into the expressions for m2 and m4:

m2 = (5x + 23)° = (5*6 + 23)° = 53°

m4 = (3x + 35)° = (3*6 + 35)° = 53°

Therefore, the measure of each angle is 53°.