Question

3 categorization 2 points
x=
no answers chosen
y=
no answers chosen
possible answers
180 118 62
73 82 47
90 121 59

Explanation:

Step1: Find the adjacent angle of \(121^{\circ}\)

Since the sum of adjacent angles on a straight line is \(180^{\circ}\), the adjacent angle of \(121^{\circ}\) is \(180 - 121=59^{\circ}\).

Step2: Use the property of isosceles triangle (two sides are equal, so two base angles are equal)

In the isosceles triangle, \(x = 180-(59 + 59)\)
\(x=180 - 118=62^{\circ}\)

Step3: Use the property of vertical angles (vertical angles are equal)

\(y\) and the adjacent angle of \(121^{\circ}\) (\(59^{\circ}\)) are not related in this way. Since the triangle has two equal sides, and using the property of parallel lines (alternate - interior angles or corresponding angles, but more directly from the triangle's angle - sum and side - angle relationship). Wait, no, another approach:
The adjacent angle of \(121^{\circ}\) is \(59^{\circ}\). In the triangle, using the angle - sum property of a triangle (\(180^{\circ}\)) for the small triangle formed. But actually, since the two lines are parallel (assumed from the arrow marks), and using the property of the triangle with two equal sides. Wait, more simply, for \(y\):
Since the two lines are parallel, and using the property of the triangle. Wait, no, actually, for \(y\), since the triangle has two equal sides (marked), and the angle adjacent to \(121^{\circ}\) is \(59^{\circ}\). Then, using the exterior - angle property or re - checking the triangle. Wait, no, correct way:
The adjacent angle of \(121^{\circ}\) is \(180 - 121=59^{\circ}\). In the isosceles triangle (two sides equal), the two base angles are equal. Let's re - express:
The sum of angles in a triangle is \(180^{\circ}\). Let the two equal angles in the isosceles triangle be \(a\). Then \(x + 2a=180\). Also, using the parallel line property (the angle \(121^{\circ}\) and the angle outside the triangle are supplementary). But another way:
Since the lines are parallel, the angle corresponding to the non - \(x\) angle in the triangle (the one adjacent to \(121^{\circ}\) after supplementary) is \(59^{\circ}\). In the isosceles triangle, \(x = 180-(59\times2)=62\). And \(y\) is equal to \(x\) (because of the parallel lines and the triangle's property. Wait, no, \(y\) and \(x\) are related as follows:
Since the two lines are parallel, and the triangle has two equal sides. Wait, no, actually, \(y=x\) (because of the property of parallel lines and the isosceles triangle. Wait, no, correct:
The adjacent angle of \(121^{\circ}\) is \(59^{\circ}\). In the isosceles triangle, \(x = 62^{\circ}\). And \(y=x\) (because of the parallel lines (alternate - interior angles for the line cutting the parallel lines and the triangle's side, and the triangle's angle equality). So \(y = 62^{\circ}\)

Answer:

\(X = 62\), \(Y = 62\)