Question

in exercises 5 - 8, find the value of x. example
5.
6.
7.
8.

Explanation:

Step1: Analyze the triangle in Exercise 5

Since all angles are equal (as indicated by the red marks), it is an isosceles triangle. In an isosceles triangle, sides opposite equal angles are equal. So \(x = 12\).

Step2: Analyze the triangle in Exercise 6

Since two angles are \(60^{\circ}\), the third angle is \(180^{\circ}-60^{\circ}-60^{\circ}=60^{\circ}\). So it is an equilateral triangle. In an equilateral triangle, all sides are equal. So \(x = 16\).

Step3: Analyze the triangle in Exercise 7

Since all sides are equal (as indicated by the red marks), it is an equilateral triangle. In an equilateral triangle, all angles are \(60^{\circ}\). So \(x + 8=60\), then \(x=60 - 8=52\).

Step4: Analyze the triangle in Exercise 8

Since all sides are equal (\(5\)), it is an equilateral triangle. In an equilateral triangle, all angles are \(60^{\circ}\). So \(3x=60\), then \(x = 20\).

Answer:

Exercise 5: \(x = 12\)
Exercise 6: \(x = 16\)
Exercise 7: \(x = 52\)
Exercise 8: \(x = 20\)