A billiard ball bounces off the sides of a rectangular billiards table in such a way that <1 is congruent to <3, <4 is congruent to <6, and <3 and <4 are complementary. If m<1 = 26.5 degrees, find m<3, m<4, m<5.
if m<1 = 26.5 degrees and <1 is congruent to <3, then m<3 = 26.5 degrees
if <3 and <4 are complementary, they'll add up to 90
90 - 26.5 = 63.5
26.5 + 63.5 = 90
so, m<4 = 63.5 degrees
if <4 is congruent to <6, then m<6 = 63.5 degrees
m<1 = 26.5 degrees
m<2 = ?
m<3 = 26.5 degrees
m<4 = 63.5 degrees
m<5 = ?
m<6 = 63.5 degrees
how would i find m<5 and m<2?
since i can't share photos, <1, <2, <3 are in one corner and <4, <5, <6 are in another, in those orders if that helps at all.
To find the measures of angles <2 and <5, we can use the properties of angles formed by parallel lines cut by a transversal.
Since <1 and <3 are congruent, and <3 and <4 are complementary, we can conclude that <1 and <4 are also congruent.
Therefore, m<4 = m<1 = 26.5 degrees.
Now, since <4 and <6 are congruent, we have m<6 = m<4 = 26.5 degrees.
Since <2 and <6 are corresponding angles formed by parallel lines, they are congruent. So, m<2 = m<6 = 26.5 degrees.
Finally, to find the measure of angle <5, we can use the fact that the sum of the angles in a triangle is 180 degrees.
The sum of angles <4, <5, and <6 is equal to 180 degrees.
Substituting in the known values, we have:
26.5 + <5 + 26.5 = 180
2(26.5) + <5 = 180
53 + <5 = 180
<5 = 180 - 53
<5 = 127 degrees.
Therefore, m<5 = 127 degrees.
To find m<5 and m<2, we need to consider the properties of angles in a rectangle.
In a rectangle, opposite angles are congruent. Therefore, <1 is congruent to <5, and <3 is congruent to <2. Since we know that m<1 = 26.5 degrees, we can conclude that m<5 is also 26.5 degrees.
Now, we can find m<2. We know that <2 and <3 are complementary angles, meaning their sum is 90 degrees. Since m<3 = 26.5 degrees, we can find m<2 by subtracting this from 90 degrees:
m<2 = 90 - 26.5 = 63.5 degrees.
To summarize:
m<1 = 26.5 degrees
m<2 = 63.5 degrees
m<3 = 26.5 degrees
m<4 = 63.5 degrees
m<5 = 26.5 degrees
m<6 = 63.5 degrees.
<2=127
<4=63.5
If the corners of the billiard table are labeled ABCD in order, then are angles 1,2,3 in corner A and angles 4,5,6 in corner C?
Remember you have right triangles formed at both corners of the table.