Question

what are the values of t and u?

Explanation:

Step1: Identify the triangle type

Since two sides of the triangle are equal (marked with red lines), it is an isosceles triangle. In an isosceles triangle, the base - angles are equal. So, \(u = 54^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \(t\) be the third angle. Then \(t+u + 54^{\circ}=180^{\circ}\). Substitute \(u = 54^{\circ}\) into the equation: \(t+54^{\circ}+54^{\circ}=180^{\circ}\).

$$t=180^{\circ}-(54^{\circ}+54^{\circ})$$

$$t = 180^{\circ}-108^{\circ}$$

$$t=72^{\circ}$$

Answer:

\(t = 72\), \(u = 54\)