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Answer :
If the measure of angle 2 is 66 degrees, the measures of the other angles include;
m∠1 = 114°
m∠2 = 66°
m∠3 = 114°
m∠4 = 66°
In Mathematics and Euclidean Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two lines intersect each other are always congruent, which means being equal to each other.
By applying the vertical angles theorem to the lines, we have the following congruent angles:
m∠1 ≅ m∠3
m∠2 ≅ m∠4
m∠2 = m∠4 = 66°
The sum of angles at a point is equal to 360 degrees;
m∠1 + m∠2 + m∠3 + m∠4 = 360
2m∠1 + 132 = 360
m∠1 = (360 - 132)/2
m∠1 = 114°
m∠3 = 114°
Complete Question:
If the measure of angle 2 is 66 degrees, what are the measures of the other angles?
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