There are two vertical angles in a figure with measures m∠1=(2x−16)° and m∠2=98° . What equation will solve for x ?
__x° -__ =__°
In a figure with two vertical angles, the vertical angles are always congruent. Therefore, we can set up the equation:
m∠1 = m∠2
(2x - 16)° = 98°
This equation can be used to solve for x.
Two intersecting lines create four angles; ∠2 and ∠4 are a vertical pair. Their sum of their measures is equal to 110° . What equation will solve for the value of each angle?
__x° =__°
If ∠2 and ∠4 are a vertical pair, then they are congruent. Let's denote their measure as x.
The sum of their measures is given as 110°, so we can set up the equation:
x + x = 110°
This equation can be used to solve for the value of each angle.
Use the image to answer the question.
An illustration shows a slanting line intersecting with two lines that appear parallel. The angles that the slanting line forms with the top line are labeled from the top left in a clockwise direction as 1, 2, 4, and 3. The angles that the slanting line forms with the bottom line are labeled from the top left in a clockwise direction as 5, 6, 8, and 7.
m∠1=125° and m∠4=(x+35)° What equation will solve for x ?
x° + __° =__°
In the given figure, ∠1 and ∠4 are vertical angles. Vertical angles are always congruent. Therefore, we can set up the equation:
m∠1 = m∠4
125° = x + 35°
This equation can be used to solve for x.
To write the equation in the requested form, we can rearrange the equation as:
x + 35° = 125°
So, the equation that will solve for x is x + 35° = 125°.
Two angles in a vertical pair have measures that add to 70° . What is the measure of each angle?
__°
In a vertical pair, the angles are congruent, which means they have the same measure.
Let x be the measure of each angle.
According to the given information, the measures of the two angles add up to 70°.
Therefore, we can set up the equation:
x + x = 70°
Simplifying the equation, we have:
2x = 70°
Now, we can solve for x by dividing both sides of the equation by 2:
x = 35°
So, each angle has a measure of 35°.
In a geometric figure two intersecting lines create four angles, where ∠1 and ∠3 are a vertical pair. If m∠1=(3x−25)° and m∠3=104° , what is the value of x ?
__
Since ∠1 and ∠3 are a vertical pair, they are congruent. We can set up the equation:
m∠1 = m∠3
(3x - 25)° = 104°
To solve for x, we can isolate x by adding 25 to both sides of the equation:
3x - 25 + 25 = 104 + 25
3x = 129
Then, we divide both sides of the equation by 3 to solve for x:
x = 129 / 3
Simplifying the expression:
x = 43
Therefore, the value of x is 43.
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 ?
3x° - 75° + 106° = 180°
3x° - 75° = 106°
3x° -75° - 106° = 180°
3x° - 75° + 106° = 90°