Triangles (types and properties)：練習問題

In an isosceles triangle, the sum of two of its angles is \(110^{\circ}\). Which of the following could be the measure of the largest angle in the triangle?

In triangle \(PQR\), \(\angle P = 2 \times \angle Q\) and \(\angle R = 3 \times \angle Q\). What is the value of \(\angle R\)?

In an isosceles triangle, the measure of the vertical angle is \(40^{\circ}\). What is the measure of each base angle?

In an isosceles triangle, if one of the base angles is \(70^{\circ}\), what is the magnitude of the vertex angle?

In triangle \(ABC\), \(\angle A = 2x^{\circ}\), \(\angle B = 3x^{\circ}\), and \(\angle C = 40^{\circ}\). Find the value of \(x\).

In triangle \(PQR\), the ratio of the interior angles \(\angle P:\angle Q:\angle R\) is \(2:3:7\). Calculate the difference between the largest angle and the smallest angle in degrees.

In triangle \(ABC\), the size of \(\angle A\) is \(50^{\circ}\) and the size of \(\angle B\) is \(65^{\circ}\).
(a) Find the size of \(\angle C\).
(b) Based on the sizes of its angles, what type of triangle is triangle \(ABC\)? Explain your answer.