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)
Since vertical angles are congruent, we have:
m∠1 = m∠2
(2x-16)° = 98°
Now we can solve for x by isolating the variable:
2x - 16 = 98
Add 16 to both sides:
2x = 114
Divide both sides by 2:
x = 57
Therefore, the equation that will solve for x is 2x - 16 = 98.
Since ∠2 and ∠4 are vertical angles, they are congruent. Let's denote their measure as x°.
The sum of the measures of ∠2 and ∠4 is equal to 110°, so we can write the equation:
x + x = 110
Simplifying the equation:
2x = 110
Now we can solve for x by isolating the variable:
Divide both sides by 2:
x = 55
Therefore, the equation that will solve for the value of each angle is x + x = 110.
Since ∠1 and ∠4 are a pair of vertically opposite angles, they are congruent. We are given that m∠1 = 125°, so we can write the equation:
m∠1 = m∠4
125° = x + 35
Now we can solve for x by isolating the variable:
Subtract 35 from both sides:
125° - 35 = x
90° = x
Therefore, the equation that will solve for x is x + 35 = 125.
Since ∠1 and ∠3 are a pair of vertically opposite angles, they are congruent. We are given that m∠1 = (3x-25)° and m∠3 = 104°.
We can set up an equation:
m∠1 = m∠3
(3x-25)° = 104°
Now we can solve for x by isolating the variable:
Add 25 to both sides:
3x - 25 + 25 = 104 + 25
3x = 129
Divide both sides by 3:
x = 43
Therefore, the value of x is 43.
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?(1 point)
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 ?