Lines, angles, and triangles：練習問題

In the figure provided, two lines intersect. If the measure of one of the angles is \(65^\circ\), what is the measure of its adjacent angle, in degrees?

In triangle \(XYZ\), the measure of \(\angle X\) is \(40^\circ\). The measure of \(\angle Y\) is \(20^\circ\) more than twice the measure of \(\angle Z\). What is the measure of \(\angle Y\)?

Triangle \(ABC\) is similar to triangle \(DEF\), where \(A\) corresponds to \(D\), \(B\) to \(E\), and \(C\) to \(F\). The ratio of the length of side \(AB\) to the length of side \(DE\) is \(2:3\). If the area of triangle \(ABC\) is 20, what is the area of triangle \(DEF\)?

In the figure, lines m and n are parallel and are intersected by a transversal t. If an interior angle on one side of the transversal measures \(72^\circ\), what is the measure, in degrees, of the other interior angle on the same side of the transversal?

In triangle \(ABC\), side \(AC\) is extended to point \(D\). If the exterior angle \(\angle BCD = 140^\circ\) and the triangle is isosceles such that side \(AB = BC\), what is the measure of angle \(\angle ABC\)?

In the figure, lines \(L\) and \(M\) are parallel and are intersected by a transversal line \(T\). If one of the alternate interior angles is represented by \((3x + 15)^{\circ}\) and its corresponding alternate interior angle on the same side of the transversal is represented by \((2x + 45)^{\circ}\), what is the value of \(x\)?

In the figure, line segment AB is parallel to line segment CD, and they are intersected by a transversal line XY at points P and Q, respectively. If the measure of an interior angle on one side of the transversal is given by \( (5x - 20)^{\circ} \) and the measure of the alternate interior angle on the opposite side of the transversal is given by \( (3x + 40)^{\circ} \), what is the value of x?

In the figure, line \( L \) is parallel to line \( M \). A transversal line \( K \) intersects both lines. If one of the angles formed by the intersection of line \( K \) and line \( L \) measures \( 7x - 15 \) degrees and its corresponding angle formed by the intersection of line \( K \) and line \( M \) measures \( 3x + 25 \) degrees, what is the value of \( x \)?

Part A: Set up the equation based on the properties of corresponding angles.
Part B: Solve for \( x \).