Question

what is the value of v?
x has 43° angle, triangle xyz with xz and yz marked as equal (isosceles triangle), angle at y is v, find v.
v = °

Explanation:

Step1: Identify triangle type

The triangle has two equal sides (marked with red ticks), so it's isosceles. In an isosceles triangle, the angles opposite equal sides are equal. Angle at \( X \) is \( 43^\circ \), and angle at \( Y \) ( \( v \)) is opposite the side equal to \( XZ \)? Wait, no—wait, the equal sides are \( YZ \) and \( XZ \)? Wait, no, the marks: side \( YZ \) and \( XZ \)? Wait, the triangle is \( XYZ \), with \( X \) at the bottom left, \( Z \) at bottom right, \( Y \) at top. The equal sides are \( YZ \) and \( XZ \)? Wait, no, the ticks: one on \( YZ \) and one on \( XZ \)? Wait, no, looking at the diagram, the two equal sides are \( XZ \) and \( YZ \)? Wait, no, the angle at \( X \) is \( 43^\circ \), and the sides \( XZ \) and \( YZ \) are equal? Wait, no, in triangle \( XYZ \), sides \( XZ \) and \( YZ \) are marked equal (red ticks), so it's an isosceles triangle with \( XZ = YZ \). Therefore, the angles opposite these sides are equal. The side \( XZ \) is opposite angle \( Y \) ( \( v \) ), and side \( YZ \) is opposite angle \( X \) ( \( 43^\circ \) ). Wait, no: in triangle \( XYZ \), side opposite angle \( X \) (at \( X \)) is \( YZ \), side opposite angle \( Y \) (at \( Y \)) is \( XZ \). Since \( XZ = YZ \), then angle \( Y \) ( \( v \)) equals angle \( X \) ( \( 43^\circ \))? Wait, no, wait: if two sides are equal, the angles opposite them are equal. So if \( XZ = YZ \), then angle at \( Y \) (opposite \( XZ \)) and angle at \( X \) (opposite \( YZ \)) are equal. So angle \( Y \) ( \( v \)) = angle \( X \) ( \( 43^\circ \))? Wait, but wait, maybe I got the sides wrong. Wait, the diagram: \( X \) is left, \( Z \) is right, \( Y \) is top. The sides with ticks: one on \( YZ \) (the right side, from \( Y \) to \( Z \)) and one on \( XZ \) (the bottom side, from \( X \) to \( Z \))? Wait, no, maybe the two equal sides are \( XY \) and \( YZ \)? No, the ticks are on \( XZ \) and \( YZ \). Wait, maybe it's an isosceles triangle with \( XZ = YZ \), so base angles at \( X \) and \( Y \) are equal? Wait, no, in a triangle, equal sides have equal opposite angles. So if \( XZ = YZ \), then angle at \( Y \) (opposite \( XZ \)) and angle at \( X \) (opposite \( YZ \)) are equal. So angle \( Y \) ( \( v \)) = angle \( X \) ( \( 43^\circ \))? Wait, but let's check the sum of angles in a triangle: \( 180^\circ \). If angle \( X \) is \( 43^\circ \), angle \( Y \) is \( v \), angle \( Z \) is... Wait, maybe I made a mistake. Wait, maybe the two equal sides are \( XY \) and \( YZ \), so it's isosceles with \( XY = YZ \), so angle at \( X \) ( \( 43^\circ \)) and angle at \( Z \) are equal? No, the diagram shows the ticks on \( XZ \) and \( YZ \). Wait, perhaps the triangle is isosceles with \( XZ = YZ \), so angle at \( X \) ( \( 43^\circ \)) and angle at \( Y \) ( \( v \)) are equal. So \( v = 43^\circ \)? Wait, but let's confirm. If two sides are equal, the angles opposite are equal. So side \( XZ \) is opposite angle \( Y \), side \( YZ \) is opposite angle \( X \). So if \( XZ = YZ \), then angle \( Y \) = angle \( X \). So \( v = 43^\circ \).

Step2: Confirm with triangle angle sum

Sum of angles in a triangle is \( 180^\circ \). If angle \( X = 43^\circ \), angle \( Y = v \), angle \( Z =? \). But if \( XZ = YZ \), then angle \( Y = angle X = 43^\circ \). So \( v = 43^\circ \).

Answer:

\( 43 \)