Question

The sum of the measures of two vertical angles is 300° solve for the measure of each angle

Answer 1

In a geometric figure 2 intersecting lines create 4 angles if <1 and <3 are a vertical pair,
m<1= (4x + 26°)
and m< 3= 98°
what is the value of x

Answer 2

for two vertical angles with measures
m<2 = (5x+ 23°) and
m<4 =(3x + 35)°
what is the measure of each angle

Answer 3

Let the measure of one angle be x. Since the sum of two vertical angles is 300 degrees, the measure of the other angle is also x.

According to the question:
x + x = 300
2x = 300
To find x, divide both sides of the equation by 2:
2x/2 = 300/2
x = 150

Therefore, Each angle measures 150 degrees.

Answer 4

If <1 and <3 are a vertical pair, it means they are congruent and their measures are equal.

Given: m<1 = (4x + 26°) and m<3 = 98°

Since <1 and <3 are congruent, we can set up an equation:
(4x + 26°) = 98°

To solve for x, we need to isolate the variable. Start by subtracting 26° from both sides of the equation:
4x = 98° - 26°
4x = 72°

Next, divide both sides of the equation by 4 to solve for x:
x = 72° / 4
x = 18°

Therefore, the value of x is 18.

Answer 5

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

m<2 = (5x + 23°)
m<4 = (3x + 35°)

Since <2 and <4 are vertical angles, their measures are equal, so we can set them equal to each other:

5x + 23° = 3x + 35°

To solve for x, subtract 3x from both sides of the equation:

5x - 3x + 23° = 3x - 3x + 35°
2x + 23° = 35°

Next, subtract 23° from both sides of the equation:

2x + 23° - 23° = 35° - 23°
2x = 12°

Finally, divide both sides of the equation by 2 to isolate x:

2x / 2 = 12° / 2
x = 6°

Now that we know the value of x, we can substitute it back into either equation to find the measure of each angle. Let's use m<2:

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

Therefore, the measure of each angle is 53°.