By definition of supplementary angles, m∠1+m∠2=180, and m∠2+m∠3=180. Then, m∠1+m∠2=m∠2+m∠3 by the property
15 answers
of equality. By subtracting m∠2 from both sides of the equation, we get m∠1 = m∠3.
what property is this?
AB+BC=AC
AB+BC=AC
The property being used here is the Transitive property of equality.
what property is this?
2x+6x+8=32
2x+6x+8=32
The property being used here is the Distributive property.
Why is it the distribuitive property?
Apologies for the incorrect response. The property being used here is the Combining Like Terms property. This property allows us to combine the terms with the same variable (in this case, 2x and 6x) by adding their coefficients to simplify the expression.
Two lines intersect at a point. The vertical angles formed are supplementary. What is the measure of each of the angles? Explain
When two lines intersect at a point, they form two pairs of opposite angles called vertical angles. These vertical angles are always congruent, meaning they have the same measure.
If the vertical angles formed by the intersection of the two lines are supplementary, it means that their measures add up to 180 degrees.
For example, let's consider angle 1 and angle 2 as the vertical angles formed by the intersection of the lines. We can express this relationship mathematically as m∠1 + m∠2 = 180, where m∠1 represents the measure of angle 1 and m∠2 represents the measure of angle 2.
Since the vertical angles are congruent, we can also express this relationship as m∠1 = m∠2.
If we substitute m∠2 for m∠1 in the first equation, we get:
m∠1 + m∠1 = 180
2m∠1 = 180
m∠1 = 90
Therefore, each of the vertical angles formed by the intersection of the lines measures 90 degrees.
If the vertical angles formed by the intersection of the two lines are supplementary, it means that their measures add up to 180 degrees.
For example, let's consider angle 1 and angle 2 as the vertical angles formed by the intersection of the lines. We can express this relationship mathematically as m∠1 + m∠2 = 180, where m∠1 represents the measure of angle 1 and m∠2 represents the measure of angle 2.
Since the vertical angles are congruent, we can also express this relationship as m∠1 = m∠2.
If we substitute m∠2 for m∠1 in the first equation, we get:
m∠1 + m∠1 = 180
2m∠1 = 180
m∠1 = 90
Therefore, each of the vertical angles formed by the intersection of the lines measures 90 degrees.
what property is ∠3+∠4=180
The property being used in ∠3 + ∠4 = 180 is the definition of supplementary angles. According to this property, if the sum of two angles is 180 degrees, then they are called supplementary angles.
what property is ∠4=180
I apologize for the confusion in my previous response. ∠4 = 180 is not a property, but rather a statement that an angle ∠4 has a measure of 180 degrees. It does not involve any particular property, but rather indicates that ∠4 is a straight angle, which is a special case where the measure is equal to 180 degrees.
what property is ∠4=110
The property being used in ∠4 = 110 is the definition of angle measurement. According to this property, angles are measured in degrees, and ∠4 specifically has a measure of 110 degrees.