In the given problem, we are asked to solve and prove that x is equal to 30°. Hence, we need to take note that we are also given with two pairs of angles namely ∠ORP and ∠ORN. These two pairs of angles are a linear pair which means that the total or summation is always equal to 180°. Thus, to complete this answer, we have the solving below:
∠ORP + ∠ORN = 180° , substitute with values such as:
80° + (3x + 10)° = 180, remove parenthesis and perform addition and subtraction of the same term such as:
80 + 3x + 10 = 180
90 + 3x = 180 , transpose 90° to the right side and perform subtraction
3x = 180 -90
3x = 90, divide both sides by 3 such as:
3x / 3 = 90/3
x = 30°
Therefore, the value of x is 30°.