Question

what are the values of u and v?

Explanation:

Step1: Use the property of isosceles triangle

Since the two sides of the triangle are equal (marked with the same tick), the triangle is isosceles. So the angles opposite to the equal sides are equal. Let's assume the two non - right angles (excluding the \(46^{\circ}\) angle) are \(x\).
We know that the sum of angles in a triangle is \(180^{\circ}\). So \(x + x+46^{\circ}=180^{\circ}\), \(2x = 180^{\circ}- 46^{\circ}=134^{\circ}\), \(x = 67^{\circ}\). But wait, we made a wrong start. Let's correct.

Step2: Use the property of triangle angle sum

Let's denote the two equal - side - opposite angles. The sum of angles in a triangle \(IJK\) is \(u + v+46^{\circ}=180^{\circ}\). Also, because the two sides (the sides adjacent to \(u\) and \(v\)) are equal (marked with the same tick), \(u = v\).
Substitute \(u = v\) into \(u + v+46^{\circ}=180^{\circ}\), we get \(2u+46^{\circ}=180^{\circ}\).

Step3: Solve for \(u\)

Subtract \(46^{\circ}\) from both sides of \(2u+46^{\circ}=180^{\circ}\): \(2u=180^{\circ}-46^{\circ}=134^{\circ}\).
Divide both sides by 2: \(u=\frac{134^{\circ}}{2}=67^{\circ}\). Since \(u = v\), \(v = 67^{\circ}\).

Answer:

\(u = 67^{\circ}\), \(v = 67^{\circ}\)