The angles of a quadrilateral are x°, ( )°x 5+ , ( )°x2 25- and ( )°x 10+ .Find the value of x

1. Break Down the Problem

We need to find the value of $x$ such that the angles of the quadrilateral add up to $360^\circ$. The angles provided are:

• $x^\circ$
• $(x + 5)^\circ$
• $(2x - 25)^\circ$
• $(x + 10)^\circ$

2. Relevant Concepts

The sum of the interior angles of a quadrilateral is given by: $\text{Sum of angles} = 360^\circ$

3. Analysis and Detail

Let's set up the equation based on the angles: $x + (x + 5) + (2x - 25) + (x + 10) = 360$

Now we simplify the equation: $x + x + 5 + 2x - 25 + x + 10 = 360$ Combining like terms: $5x - 10 = 360$

Next, we solve for $x$:

1. Add 10 to both sides: $5x = 370$
2. Divide by 5: $x = 74$

4. Verify and Summarize

To verify, we substitute $x = 74$ back into the expressions for the angles:

• $x = 74^\circ$
• $x + 5 = 79^\circ$
• $2x - 25 = 2(74) - 25 = 148 - 25 = 123^\circ$
• $x + 10 = 84^\circ$

Calculating the total: $74 + 79 + 123 + 84 = 360$ This confirms that our calculations are correct.

Final Answer

The value of $x$ is $74$.