If the angles of a quadrilateral are (3y + 10)°, (2y + 30)°, (y + 20)° and 4y°. Find the value of y.

1. Analyze the question

You are given the four interior angles of a quadrilateral in terms of a variable $y$. You need to find the value of $y$ by applying the geometric property of quadrilaterals.

2. Explain the concept

The fundamental principle here is that the sum of the interior angles of any quadrilateral is always 360°. If the angles are $A, B, C,$ and $D$, then:

3. Show the solution

Step 1: Set up the equation. Sum the given expressions and set them equal to 360:

Step 2: Group the like terms. Combine the terms with $y$ and the constant numbers separately:

Step 3: Simplify the equation.

Step 4: Solve for $y$. Subtract 60 from both sides:

Divide by 10:

4. Identify the answer

The value of $y$ is 30. Looking at the options provided, this corresponds to Option C.

5. Tip

When dealing with polygons, remember the formula for the sum of interior angles: $(n - 2) \times 180^\circ$, where $n$ is the number of sides. For a quadrilateral, $n=4$, so $(4-2) \times 180 = 2 \times 180 = 360^\circ$. This formula works for any polygon, whether it's a triangle, pentagon, or hexagon!