Question

what are the values of v and w?
work it out
not feeling ready yet? these can help:
triangle angle - sum theorem
classify triangles

Explanation:

Step1: Identify the triangle type

Since two sides of the triangle \( \triangle XYZ \) are marked as equal, it is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. So, \( v=\angle X=\angle Z \) (angles opposite equal sides \( YZ \) and \( XY \)).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \( 180^{\circ} \). Let \( v = x \), then \( w=x \) (from Step 1). We know that \( x + x+52^{\circ}=180^{\circ} \).
Combining like terms gives \( 2x+52^{\circ}=180^{\circ} \).
Subtract \( 52^{\circ} \) from both sides: \( 2x=180^{\circ}- 52^{\circ}=128^{\circ} \).
Divide both sides by 2: \( x = v=\frac{128^{\circ}}{2}=64^{\circ} \).

Step3: Calculate \( w \)

Since \( w = v \) (from Step 1), \( w = 64^{\circ} \).

Answer:

\( v = 64^{\circ} \), \( w = 64^{\circ} \)