Exercise 6.2
1. Find the value of the unknown exterior angle x in the following diagrams:
a
(i) Find the value of x in the following diagram.
(i)
According to the exterior angle property, the
Hence,
x = 70° + 50° =
The value of x is 120°.
b
(ii) Find the value of x in the following diagram.
(ii)
Solution:
According to the exterior angle property,the sum of the opposite non-adjacent interior angles equals the exterior angle of a triangle.
Hence,
x = 65° +
The value of x is 110°.
c
(iii) Find the value of x in the following diagram.
(iii)
Solution:
According to the exterior angle property, the sum of the opposite non-adjacent interior angles equals the exterior angle of a triangle.
Hence,
x = 30° +
The value of x is 70°.
d
(iv) find the value of x in the following diagram.
(iv)
Solution:
According to the exterior angle property, the sum of the opposite non-adjacent interior angles equals the exterior angle of a triangle.
Hence,
x = 60° + 60° =
The value of x is 120°.
e
(v) Find the value of x in the following diagram.
(v)
Solution:
According to the exterior angle property, the sum of the opposite non-adjacent interior angles equals the exterior angle of a triangle.
Hence,
x = 50° +
The value of x is 100°.
f
(vi) Find the value of x in the following diagram.
(vi)
Solution:
According to the exterior angle property, the sum of the opposite non-adjacent interior angles equals the exterior angle of a triangle.
Hence,
x = 30° +
The value of x is 90°.
2. Find the value of the unknown interior angle x in the following figures.
According to the exterior angle property, the sum of the opposite non-adjacent interior angles equals the exterior angle of a triangle.
a
(i) Find the value of x in the following diagram.
(i)
Solution:
x +
Subtract 50° from both sides of the equation.
x =
The value of x is 65°.
b
(ii) Find the value of x in the following diagram.
(ii)
Solution:
x +
Subtract 70° from both sides of the equation.
x = 100° − 70° =
The value of x is 30°.
c
(iii) Find the value of x in the following diagram.
(iii)
Solution:
x +
Subtract 90° from both sides of the equation.
x + 90° − 90° = 125° − 90° =
The value of x is 35°.
d
(iv) Find the value of x in the following diagram.
(iv)
Solution:
x +
Subtract 60° from both sides of the equation.
x + 60° − 60° = 120° − 60° =
The value of x is 60°.
e
(v) Find the value of x in the following diagram.
(v)
Solution:
x +
Subtract 30° from both sides of the equation.
x + 30° − 30° = 80° − 30° =
The value of x is 50°.
f
(vi) Find the value of x in the following diagram.
(vi)
Solution:
x +
Subtract 35° from both sides of the equation.
x + 35° − 35° = 75° − 35° =
The value of x is 40°.