In the given diagram, we have a triangle with two angles labeled as (3x + 10)° and (4x - 30)°. We need to solve for the value of x.
To find the value of x, we can use the property that the sum of the interior angles of a triangle is always 180 degrees. Therefore, we can set up the equation:
(3x + 10) + (4x - 30) + 90 = 180
Let's simplify the equation step by step:
Combine like terms:
3x + 4x + 10 - 30 + 90 = 180
7x + 70 = 180
Next, isolate the variable term by subtracting 70 from both sides:
7x + 70 - 70 = 180 - 70
7x = 110
To solve for x, divide both sides of the equation by 7:
(7x)/7 = 110/7
x = 15.71
Therefore, the value of x is approximately 15.71.
Please note that this solution assumes the given diagram accurately represents the angle measurements, and the calculations provided are based on that assumption.