Question

what are the values of u and v?

u =

v =

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work it out

not feeling ready yet? these can help:

triangle angle - sum theorem

Explanation:

Step1: Identify the triangle type

Since two sides are equal (marked with red ticks), it is an isosceles triangle. In an isosceles triangle, the base - angles are equal. So \(u = 55^{\circ}\).

Step2: Use the triangle angle - sum theorem

The sum of angles in a triangle is \(180^{\circ}\). Let \(v\) be the third angle. Then \(u + 55^{\circ}+v=180^{\circ}\). Substitute \(u = 55^{\circ}\) into the equation: \(55^{\circ}+55^{\circ}+v = 180^{\circ}\).
Simplify the left - hand side: \(110^{\circ}+v=180^{\circ}\).
Solve for \(v\): \(v=180^{\circ}-110^{\circ}=70^{\circ}\).

Answer:

\(u = 55\), \(v = 70\)