If M and N are parallel and angle 1 is 135° , what is the sum of angle 6 and angle 8?
(1 point)
The sum of angle 6 and angle 8 is equal to 180°. This is because angle 6 and angle 8 are corresponding angles, and corresponding angles formed by a transversal cutting two parallel lines are congruent. Therefore, since angle 6 is equal to 135°, angle 8 must be equal to 45°. Therefore, the sum of angle 6 and angle 8 is 135° + 45° = 180°.
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To find the sum of angle 6 and angle 8, we need to determine the measures of those angles.
Given that M and N are parallel lines, we can use the alternate interior angles theorem. According to this theorem, when a transversal intersects two parallel lines, the alternate interior angles are congruent.
In this case, angle 1 and angle 8 are alternate interior angles. Since angle 1 measures 135°, angle 8 also measures 135°.
Now, angle 6 is an alternate interior angle with angle 8. Therefore, angle 6 and angle 8 are congruent, and both have a measure of 135°.
Therefore, the sum of angle 6 and angle 8 is 135° + 135° = 270°.
To find the sum of angle 6 and angle 8, we need to determine their values.
In the given description, it is mentioned that M and N are parallel lines. When a transversal, like the line containing angles 1, 6, and 8, intersects two parallel lines, certain angle relationships are formed.
One important relationship is that the corresponding angles are congruent. This means that angles that are in the same position relative to the transversal (in this case, angles 1 and 6, and angles 1 and 8) will have the same measure. Therefore, angle 6 is also 135°.
Knowing that angles 1 and 6 are congruent, we can conclude that the sum of angles 6 and 8 is equal to the sum of angles 1 and 8. So, to find the sum of angle 6 and angle 8, we need to find the measure of angle 8.
To find the measure of angle 8, we can use the fact that angles that are opposite each other when two parallel lines are intersected by a transversal are also congruent. In this case, angles 1 and 8 are opposite angles. Since we know angle 1 is 135°, angle 8 will also be 135°.
Therefore, the sum of angle 6 and angle 8 is:
angle 6 + angle 8 = 135° + 135° = 270°
So, the sum of angle 6 and angle 8 is 270°.