Question

1. the measures of the interior angles of a quadrilateral are $2x + 10$, $3x$, $3x + 5$, and $5x + 20$. what is the value of $x$?

a. 35
b. 25
c. 13
d. 12

Explanation:

Step1: Recall quadrilateral angle sum

The sum of interior angles of a quadrilateral is \(360^\circ\). So, we set up the equation: \((2x + 10) + 3x + (3x + 5) + (5x + 20) = 360\).

Step2: Combine like terms

Combine the \(x\)-terms and constant terms: \(2x + 3x + 3x + 5x + 10 + 5 + 20 = 360\) → \(13x + 35 = 360\).

Step3: Solve for \(x\)

Subtract 35 from both sides: \(13x = 360 - 35 = 325\). Then divide by 13: \(x = \frac{325}{13} = 25\).

Answer:

B. 25