Two intersecting lines create four angles; ∠1 and ∠3 are a vertical pair. Their sum of their measures is equal to 68° . What equation solves for the value of each angle?(1 point)
Since ∠1 and ∠3 are a vertical pair, their measures are equal.
We are given that m∠1 = (4x + 26)° and m∠3 = 98°.
According to the given information, we can set up the equation:
(4x + 26)° = 98°
Now, we can solve this equation for x:
4x + 26 = 98
Subtracting 26 from both sides:
4x = 98 - 26
4x = 72
Dividing both sides by 4:
x = 72/4
x = 18
Therefore, the value of x is 18.
Since ∠2 and ∠4 are a vertical pair, their measures are equal.
We are given that m∠2 = (5x + 23)° and m∠4 = (3x + 35)°.
According to the given information, we can set up the equation:
(5x + 23)° = (3x + 35)°
Now, we can solve this equation for x:
5x + 23 = 3x + 35
Subtracting 3x from both sides:
5x - 3x + 23 = 35
2x + 23 = 35
Subtracting 23 from both sides:
2x = 35 - 23
2x = 12
Dividing both sides by 2:
x = 12/2
x = 6
Now that we know the value of x, we can substitute it back into either equation to find the measures of ∠2 and ∠4:
m∠2 = (5x + 23)° = (5*6 + 23)° = 53°
m∠4 = (3x + 35)° = (3*6 + 35)° = 53°
Therefore, the measure of each angle, ∠2 and ∠4, is 53°.
The sum of measures of vertically opposite angles is always equal. Therefore, we can say that ∠1 = ∠3.
Let's assume the measures of ∠1 and ∠3 as x.
Therefore, we can write the equation as:
x + x = 68°
2x = 68°
Dividing both sides of the equation by 2:
x = 34°
So, the measure of each angle, ∠1 and ∠3, is 34°.
The sum of the measures of two vertical angles is 300° . Solve for the measure of each angle.(1 point)
Let's assume the measures of the two vertical angles as x and y.
Since the sum of the measures of two vertical angles is always equal, we can write the equation as:
x + y = 300°
No solution can be determined without additional information about the relationship between x and y.
The sum of the measures of two vertical angles is 300° . Solve for the measure of each angle.(1 point) Responses 75° 75 degrees 120° 120 degrees 150° 150 degrees 90°
Let's assume the measures of the two vertical angles as x and y.
Since the sum of the measures of two vertical angles is always equal, we can write the equation as:
x + y = 300°
Since we don't have any additional information about the specific values of x and y, we can't solve for their exact measures. However, we can list some possible pairs of measures that satisfy the equation:
- x = 75°, y = 225°
- x = 120°, y = 180°
- x = 150°, y = 150°
- x = 90°, y = 210°
These are just a few examples of pairs of angles whose measures add up to 300°. There are infinitely many other possible combinations.