Question

what are the values of y and z?
d
60°
z
c
y
b
y =
°
z =
°

Explanation:

Step1: Identify the triangle type

Since two sides of the triangle are equal (marked with the same tick), it is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. So \(y = z\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So \(y+z + 60^{\circ}=180^{\circ}\). Substitute \(y = z\) into the equation: \(y + y+60^{\circ}=180^{\circ}\), which simplifies to \(2y=180^{\circ}- 60^{\circ}\). Then \(2y = 120^{\circ}\), and \(y=\frac{120^{\circ}}{2}=60^{\circ}\). Since \(y = z\), \(z = 60^{\circ}\) as well.

Answer:

\(y = 60\), \(z = 60\)