Certainly! I'll be happy to solve and explain the given problem to you in a step-by-step manner.
In the given diagram, we have a triangle with two angles labeled as 4x° and (3x + 10)°. We need to solve for the value of x.
According to the properties of triangles, the sum of the interior angles of a triangle is always 180 degrees. Therefore, we can set up the following equation:
4x + (3x + 10) + 90 = 180
Let's simplify the equation:
4x + 3x + 10 + 90 = 180
7x + 100 = 180
Next, we'll isolate the variable term by subtracting 100 from both sides of the equation:
7x = 180 - 100
7x = 80
To solve for x, we'll divide both sides of the equation by 7:
x = 80 / 7
Now, let's calculate the value of x:
x ≈ 11.43
Therefore, the value of x is approximately 11.43.
Please note that this solution assumes the given diagram accurately represents the angle measurements, and the calculations provided are based on that assumption.