Question

what is the value of a?

Explanation:

Step1: Identify the triangle type

The triangle \( \triangle TUS \) is isosceles because two sides are marked as equal. In an isosceles triangle, the base - angles are equal. Let \( \angle T=\angle U = a\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). So, \(a + a+54^{\circ}=180^{\circ}\).
Simplify the equation: \(2a+54^{\circ}=180^{\circ}\).
Subtract \(54^{\circ}\) from both sides: \(2a=180^{\circ}- 54^{\circ}=126^{\circ}\).
Divide both sides by 2: \(a=\frac{126^{\circ}}{2}=63^{\circ}\).

Answer:

\(63\)