Question 84: The given triangle is an isosceles triangle. We have measure angle 2 = measure angle 3 We are given that angle 1 = 70° We know that the sum of the interior angles of the triangle is 180. This means that: 180 = angle 1 + angle 2 + angle 3 180 = 70 + angle 2 + angle 3 angle 2 + angle 3 = 110 Since both angles are equal, therefore: measure angle 2 = 110/2 = 55° We are given that: measure angle 2 = x + 64 This means that: x + 64 = 55 x = 55 - 64 x = -9
Question 85: The given triangle is an isosceles triangle. We have the two base angles are equal. Since one of them is 30°, this means that the other is also 30° We know that the sum of the interior angles of the triangle is 180. This means that: 180 = angle 1 + angle 2 + angle 3 180 = 30 + angle 2 + 30 angle 2 = 120 We are given that: measure angle 2 = 14x - 6 This means that: 14x - 6 = 120 14x = 126 x = 126/14 x = 9
Question 86: The given triangle is an isosceles triangle. We have the two base angles are equal. Since one of the base angles is 40° This means that the other one is also 40° Therefore: measure angle 2 = 40° We are given that: measure angle 2 = 47 + x This means that: 47 + x = 40 x = 40 - 47 x = -7
Question 87: The given triangle is an equilateral triangle. This means that all three interior angles are equal and each is measuring 60°. Therefore: measure angle 2 = 60° We are given that: measure angle 2 = x + 71 This means that: x + 71 = 60 x = 60 - 71 x = -11
