Use the figure to answer the question.
An illustration shows a right inclined transversal passing through two parallel lines labeled upper M and upper N. Four angles are formed at the intersections of the transversal with upper M and upper N. The angles formed around the intersection point of the transversal and upper M are labeled clockwise, starting from the upper left quadrant: 1, 2, 4, and 3. The corresponding angles formed around the intersection point of upper N are labeled clockwise, starting from the upper left quadrant: 5, 6, 8, and 7.
If M and N are parallel and angle 1 is 135° , what is the sum of angle 6 and angle 8?
Since line M is parallel to line N, angles 1 and 6 are corresponding angles. Corresponding angles are congruent when lines are parallel, so angle 6 is also 135°.
Similarly, angle 4 and angle 7 are corresponding angles, and since angle 4 is 135°, angle 7 is also 135°.
The sum of angle 6 and angle 8 is 135° + 135° = 270°. Answer: \boxed{270}.
2 and 8 are 40 4 and 7 are 135 so whats the answer because 270 is not it
Apologies for the mistake in the previous response. Let's reconsider the problem:
From the given information, we know that angle 1 is 135°.
Since angles 1 and 5 are corresponding angles, we can conclude that angle 5 is also 135°.
Angles 5 and 6 are vertically opposite angles, which means they are congruent. Therefore, angle 6 is also 135°.
Similarly, angles 4 and 8 are corresponding angles. Since angle 4 is 40°, we can conclude that angle 8 is also 40°.
The sum of angle 6 and angle 8 is 135° + 40° = 175°.
Therefore, the correct answer is \boxed{175}.
Since line M and line N are parallel, we know that angle 1 and angle 6 are corresponding angles, and angle 1 is given as 135°. Corresponding angles are equal when a transversal intersects parallel lines.
Therefore, angle 6 will also be 135°.
Now, we need to find the value of angle 8 in order to calculate the sum of angle 6 and angle 8.
By the same logic, angle 8 and angle 3 are corresponding angles because they are formed between the same parallel lines and the same transversal.
Since angle 3 and angle 1 form a linear pair (they are adjacent angles that add up to 180°), we can find angle 3 by subtracting angle 1 from 180°:
180° - 135° = 45°
Therefore, angle 8 is equal to angle 3, which is 45°.
Finally, the sum of angle 6 and angle 8 is:
135° + 45° = 180°
So, the sum of angle 6 and angle 8 is 180°.
To find the sum of angle 6 and angle 8, we need to analyze the properties of parallel lines and transversals.
In the given figure, we have two parallel lines, M and N, with a right-inclined transversal intersecting them.
From the information given, we know that angle 1 measures 135°. Angle 1 is formed at the intersection of the transversal and line M.
To find the measure of angle 6, we look for its corresponding angle on the same side of the transversal and parallel line N. In this case, angle 6 corresponds to angle 3.
By the properties of parallel lines and transversals, we know that corresponding angles are congruent. Therefore, angle 3 measures 135°.
Similarly, to find the measure of angle 8, we look for its corresponding angle on the same side of the transversal and parallel line N. In this case, angle 8 corresponds to angle 4.
Again, by the properties of parallel lines and transversals, we know that corresponding angles are congruent. Therefore, angle 4 measures 135°.
Now, to find the sum of angle 6 and angle 8, we add their measures:
Angle 6 + Angle 8 = Angle 3 + Angle 4 = 135° + 135° = 270°
Therefore, the sum of angle 6 and angle 8 is 270°.