By the definition of complementary angles, since angle 1 is complementary to angle 2, we know that the measure of angle 1 plus the measure of angle 2 equals 90 degrees. This can be represented as m(angle 1) + m(angle 2) = 90 degrees. In addition, we are given that angle 4 is congruent to angle 1, meaning that they have the same measure. Thus, m(angle 4) = m(angle 1) = 40 degrees.
Using the vertical angles theorem, we can conclude that angle 2 and angle 4 are congruent. This can be represented as m(angle 2) = m(angle 4). Furthermore, since angle 4 is congruent to angle 1, we can substitute m(angle 1) in place of m(angle 4) in the equation, resulting in m(angle 2) = m(angle 1).
Combining the given equation m(angle 1) + m(angle 2) = 90 degrees with the substitution property of equality, we find that m(angle 1) + m(angle 1) = 90 degrees. Simplifying this equation, we get 2(m(angle 1)) = 90 degrees.
To solve for m(angle 1), we divide both sides of the equation by 2, giving us m(angle 1) = 45 degrees. Therefore, the measure of angle 1 is 45 degrees.
Finally, using the angle bisector theorem, we can conclude that the angles created by the bisecting horizontal line are congruent. Thus, m(angle 3) = m(angle 1) and m(angle 4) = m(angle 1) = 45 degrees.
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Given:
is complementary to
Prove:
Two lines intersect each other. Another horizontal line bisects to create angles 1,2 and 3, 4
Complete the proof in paragraph form.
Given angle 1 is complementary to angle 2 is pointing to m angle 1 plus m angle 2 equals 90 degrees pointing to the blank box and another blank box. And angle 4 congruent angle 1 also pointing m angle 4 equals m angle 1 pointing down 40 degrees
Complete the proof in paragraph form.
By the definition of complementary angles, since
is complementary to
,
. By the vertical angles theorem,
, and
by the definition of congruence. Combined with the given equation,
, the substitution property of equality means that
. Using the
,
. Finally, using the
,
.
1 answer
1 answer