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
Hope this helps :)