Given m, \parallel, nm∥n, find the value of x and y.
m
n
x°
47°
y°
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Answer
Since m is parallel to nm, the angles x° and 47° are corresponding angles. Therefore, x° = 47°.
Similarly, since nm is parallel to n, the angles y° and 47° are alternate interior angles. Therefore, y° = 47°.
So, the value of x is 47° and the value of y is 47°.
try again.
Since m is parallel to nm, the angles x° and 47° are corresponding angles. Therefore, x° = 47°.
Similarly, since nm is parallel to n, the angles y° and 47° are also corresponding angles. Therefore, y° = 47°.
So, the value of x is 47° and the value of y is also 47°.
nope
Apologies for the incorrect response. Let's try again to find the correct values of x and y.
Given that m is parallel to nm and nm is parallel to n, we can conclude that x° and 47° are corresponding angles and y° and 47° are alternate interior angles.
Therefore, we have the following equations:
x° = 47° (corresponding angles)
y° + 47° = 180° (interior angles of a triangle sum to 180°)
From the equation y° + 47° = 180°, we can subtract 47° from both sides:
y° = 180° - 47°
y° = 133°
Therefore, the value of x is 47° and the value of y is 133°.
To find the values of x and y, we will need to use the properties of parallel lines and transversals.
First, let's identify the angles formed by the parallel lines and the transversal:
Angle m° is provided in the question.
Angle n° is congruent to angle m° since the given lines are parallel.
Angle x° is an exterior angle formed by the transversal intersecting lines m and n. The sum of the remote interior angles (x° and m°) is equal to 180°. Therefore, we can find the value of x by subtracting 47° from 180°:
x° = 180° - 47° = 133°.
Similarly, angle y° is another exterior angle formed by the transversal intersecting lines m and n. The sum of the remote interior angles (y° and n°) is equal to 180°. Since n° is congruent to m°, we can use the value of m° to find y°:
y° = 180° - m° = 180° - 47° = 133°.
So, the values of x and y are both 133°.