Question

what is the value of a? 120° a = °

Explanation:

Step1: Identify Triangle Type

The triangle \( WXY \) has two equal sides (marked with red ticks), so it's isosceles with \( WX = WY \)? Wait, no—wait, the equal sides are \( XY \) and \( WY \)? Wait, no, the marks: one on \( XY \) and one on \( WY \)? Wait, no, looking at the diagram, the two sides with ticks are \( WY \) and \( XY \)? Wait, no, actually, in triangle \( WXY \), sides \( WY \) and \( XY \) are marked equal? Wait, no, the vertex \( X \) to \( Y \) and \( W \) to \( Y \)? Wait, no, the triangle has vertices \( W \), \( X \), \( Y \). The side \( XY \) and \( WY \) have ticks? Wait, no, maybe \( WX \) and \( WY \)? Wait, no, the angle at \( Y \) is \( 120^\circ \). In an isosceles triangle, the base angles are equal. Wait, if two sides are equal, then the angles opposite them are equal. Wait, let's correct: in triangle \( WXY \), sides \( WY \) and \( XY \) are equal (marked with ticks), so the triangle is isosceles with \( WY = XY \). Therefore, the angles opposite these sides: angle at \( W \) (opposite \( XY \)) and angle at \( X \) (opposite \( WY \)) are equal? Wait, no: side \( WY \) is opposite angle \( X \), and side \( XY \) is opposite angle \( W \). So if \( WY = XY \), then angle \( X \) (which is \( a \)) and angle \( W \) are equal? Wait, no, the angle at \( Y \) is \( 120^\circ \), which is the vertex angle. So the sum of angles in a triangle is \( 180^\circ \). So angle \( Y = 120^\circ \), so angles \( X \) and \( W \) sum to \( 180 - 120 = 60^\circ \). And since the triangle is isosceles with \( WY = XY \), angles \( X \) and \( W \) are equal. Therefore, each is \( 60^\circ / 2 = 30^\circ \). Wait, let's recheck:

Sum of angles in triangle: \( \angle W + \angle X + \angle Y = 180^\circ \)

Given \( \angle Y = 120^\circ \), so \( \angle W + \angle X = 60^\circ \)

Since \( WY = XY \) (marked equal), triangle is isosceles with \( \angle W = \angle X \) (angles opposite equal sides)

Therefore, \( \angle X = a = \frac{60^\circ}{2} = 30^\circ \)

Step2: Calculate \( a \)

Using the angle sum property: \( 180 - 120 = 60 \), then divide by 2 (since two angles are equal) gives \( 30 \).

Answer:

\( 30 \)