The values of x , m∠ A and m ∠B are 30. 6, 108. 4 and 71. 2 respectively.
How to determine the parameters
From the information given, we have that:
- ∠A and ∠B are supplementary
- m ∠A = 4x - 14
- m ∠B = 2x + 10
It is important to note that supplementary angles sum up to 180 degrees
So, we have that
m ∠A + m∠ B = 180
Substitute the values
4x - 14 + 2x + 10 = 180
collect like terms
4x + 2x - 14 + 10 = 180
Add like terms
6x - 4 = 180
Make 'x' the subject
6x = 180 + 4
6x = 184
x = 184/ 6
x = 30. 6
m∠ A = 4x - 14 = 4 ( 30. 6) - 14 = 108. 4
m ∠B = 2x + 10 = 2( 30. 6) + 10 = 71. 2
Thus, the values of x , m∠ A and m ∠B are 30. 6, 108. 4 and 71. 2 respectively.
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