Answer:
By the given diagram,
PLM is a triangle,
K and N are points on line MN,
m∠KLP = 3x, m∠P = x, m∠PMN = 2x + 72°
We need to give the reasons in the steps of finding the value of x.
For this we have to know the following properties :
Linear pairs: Adjacent angles which are supplementary.
Subtraction property of equality : We can subtract a number or expression in both sides of an equation.
i.e. a = b ⇒ a + c = b + c
Exterior angle theorem : exterior angle formed by extending the side of a triangle is equal to the sum of its non-adjacent angles.
Thus, the steps of finding value of x are as follow,
1. m∠KLP+m∠PLM = 180° ( linear pairs )
2. 3x +m∠PLM = 180° ( Substitution)
3. m∠PLM = 180° - 3x ( Subtraction property of equality)
4. m∠PMN=m∠P+m∠PLM ( Exterior angle theorem )
5. 2x + 72° = x + 180° - 3x ( Substitution)
6. 2x + 72° = 180° - 2x ( Solving )
2x = 180° - 2x - 72°
2x + 2x = 108°
4x = 108°
x = 27°