There are two vertical angles in a figure with measures m∠1=(2x−16)° and m∠2=98° . What equation will solve for x ?(2 points)
The sum of the measures of two vertical angles is always equal. So we have:
m∠1 + m∠2 = 180°
Substituting the given values, we get:
(2x - 16) + 98 = 180
Simplifying the equation:
2x + 82 = 180
To solve for x, we subtract 82 from both sides of the equation:
2x = 98
Dividing by 2:
x = 49
Therefore, the equation that will solve for x is: 2x + 82 = 180.
wrong
Apologies for the mistake. Since vertical angles are congruent, we can set the measures of the two angles equal to each other:
(2x - 16)° = 98°
To solve for x, we need to isolate it. Adding 16 to both sides:
2x = 114
Dividing both sides by 2:
x = 57
Therefore, the equation that solves for x is: (2x - 16)° = 98°.
yes thats correct
Thank you for confirming. If you have any more questions, feel free to ask.
There is a pair of vertical angles whose measures are m∠1=106° and m∠2=(3x−75)° . What equation can you write to solve for x ?(1 point
Since vertical angles are congruent, we can set the measures of the two angles equal to each other:
m∠1 = m∠2
106° = (3x - 75)°
To solve for x, we need to isolate it. Adding 75 to both sides:
106° + 75° = 3x°
181° = 3x°
Dividing both sides by 3:
60.33° ≈ x°
Therefore, the equation that can be written to solve for x is: 106° = (3x - 75)°.
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)
Let's start by setting up the equation using the given information:
∠1 + ∠3 = 68°
Since ∠1 and ∠3 are vertical angles, they are congruent. We can rewrite the equation as:
∠1 + ∠1 = 68°
Simplifying the equation:
2∠1 = 68°
To solve for ∠1, we divide both sides of the equation by 2:
∠1 = 34°
Since ∠1 and ∠3 are congruent, ∠3 is also 34°.
Therefore, the equation that solves for the value of each angle is: ∠1 = ∠3 = 34°.
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)
Responses
2x°+68°=180° 2 x plus 68 degrees equals 180 degrees
x°=68°
x equals 68 degrees
2x°=68°
2 x equals 68 degrees
68x°=2°
Apologies for the confusion. Let's approach the problem again.
Given that ∠1 and ∠3 are a vertical pair, their measures are equal. Let's assume that the measure of both angles is x.
So we have the equation:
∠1 + ∠3 = 68°
Since ∠1 and ∠3 are congruent, we can rewrite the equation as:
x + x = 68°
Simplifying the equation:
2x = 68°
To solve for x, we divide both sides of the equation by 2:
x = 34°
Therefore, the equation that solves for the value of each angle is: ∠1 = ∠3 = 34°.