Question

what is the value of s?
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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 base - angles are equal.

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let the two equal angles be \(A\) and \(C\) (since \(AB = AC\)). We know that \(\angle B=74^{\circ}\).
Using the formula \(\angle A+\angle B+\angle C = 180^{\circ}\), and since \(\angle A=\angle C\) (isosceles triangle property), we can substitute \(\angle A\) with \(\angle C\). So, \(2\angle C+74^{\circ}=180^{\circ}\).
First, subtract \(74^{\circ}\) from both sides of the equation: \(2\angle C=180^{\circ}- 74^{\circ}\).
\(2\angle C = 106^{\circ}\).
Then divide both sides by 2: \(\angle C=\frac{106^{\circ}}{2}\).

Answer:

\(53\)