Two angles in a vertical pair have measures that add to 70° . What is the measure of each angle?
By definition, vertical angles are two nonadjacent angles formed by two intersecting lines. These angles are congruent, meaning they have the same measure. Since the measure of the two angles in a vertical pair is 70°, each angle must have a measure of 70°.
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Let's assume one angle in the vertical pair has measure x°. Since vertical angles are congruent, the other angle has measure x° as well.
According to the given information, the two angles' measures add up to 70°. So we can set up the equation:
x + x = 70
Combining like terms:
2x = 70
Dividing both sides by 2:
x = 35
Therefore, each angle in the vertical pair 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 ?(1 point)
Since angles 1 and 3 form a vertical pair, they are congruent. Therefore, we can set up an equation:
m∠1 = m∠3
(3x - 25)° = 104°
Now we can solve for x:
3x - 25 = 104
Adding 25 to both sides:
3x = 129
Dividing both sides by 3:
x = 43
Therefore, the value of x is 43.