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
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
The property being used here is the Transitive property of equality.
what property is this?
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.